
























Class 

Book. 


H£333 


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102-3 


COPYRIGHT DEPOSIT. 


























A PRACTICAL COURSE 


IN 

ROOF FRAMING 


The Underlying Principles and Their 
Application to Practical Work 


Especially Written for Foremen, Journeymen 
and Apprentice Woodworkers, and 
as a Text Book for Schools 

by • 

RICHARD M." VAN GAASBEEK 

H'Ad of Department of Woodworking - , School of Science and 
Technology, Pratt Institute, Brooklyn, N. Y. 

Author of 

“A Practical Course in Wooden Boat and Shipbuilding” 

Second Edition 
Revised and Enlarged 


FULLY ILL US TRA TED 


y » 


CHICAGO 

FREDERICK J. DRAKE & COMPANY 
Publishers 












TH Zj3<?3 
}h 


Copyright, 1920 and 1923 
By Frederick J. Drake & Co., 
Chicago 


All Rights Reserved 




Printed in the United States of America 


J)CT -5 1923 

©C1A7G02 2 8 







PREFACE 


This text is prepared to afford practical instruction 
for foremen, journeymen and apprentices wishing* to 
. qualify for advanced positions or to become builders. 

The instruction is arranged to give house carpenters 
and other woodworkers a practical knowledge ot the 
steel square and its uses and to develop a broader 
understanding of fundamental principles and their ap¬ 
plication to practical work. 

The problems and drawings illustrating the text were 
developed in the carpenter shop of Pratt Institute, 
Brooklyn, N. Y. They represent typical everyday 
jobs and offer a variety of simple and complicated 

roofs for practice purposes. 

The study is intended to be broader in its applica¬ 
tion than the title implies. It is one of the best sub¬ 
jects that can be used to demonstrate the many uses 
of the steel square. The course explains the various 
figures on the blade and tongue and encourages the use 
of them. It also offers students an excellent oppor¬ 
tunity to learn plan reading and laying out. It requires 
and teaches them to think mechanically and it materially 
aids them in solving unusual problems encountered in 
practicing their trade. 

By the term “plan reading” is not meant the taking 
off of measurements as generally implied, but the pic¬ 
turing in the mind of the mechanical construction of 
a project from a design submitted by an architect or 

3 


4 


COURSE IN ROOF FRAMING 


owner. This foresight and an understanding of trade 
principles are both essential requirements in qualifying 
mechanics to make intelligent shop layouts. This is an 
art that a great many do not possess, but one that can 
be and should be acquired. 

The layout for a roof is a view from above, looking 
down. It shows the center lines of the rafters in the 
plan, which is a flat level surface. In picking up the 
bevels and measurements from the plan, mechanics 
forget that they must also be applied on the same 
plane or relative position. They have trouble in under¬ 
standing that the bevels and measurements taken from 
the plan cannot be applied on the top edge of the rafter 
stock, which, in its relative position, forms the pitch 
of the roof. It is not easy for them to picture in their 
minds a roof in elevation while looking at it in plan or 

on the lavout. 

«/ 

The author purposely avoids using complicated dia¬ 
grams: realizing that, to be practical, the solution of a 
problem must first of all be simple and easy to under¬ 
stand. More important still, it must be easy to remem¬ 
ber when once solved. Simple practical methods that 
can be easily understood and mastered are used through¬ 
out the text. 

The author’s preparation for writing the text dates 
back to the time when he was associated with the late 
Mr. Edward M. Healy, then head of the Department 
of Woodworking, Pratt Institute, Brooklyn, N. Y. It 
was Mr. Healy’s enthusiasm for the subject that in¬ 
spired the author to continue in the development of the 
work left unfinished. The author wishes to avail him- 


PREFACE 


5 


self of this opportunity of expressing liis grateful ac¬ 
knowledgment to Mr. Anson W. Smith, formerly in¬ 
structor in Mechanical Drawing, Pratt Institute, for en¬ 
couragement and many suggestions in the preparation of 
the drawings illustrating the text, and to his associate, 
Mr. Joseph A. Shelly, for helpful criticisms during the 
development of the course. 

The Author. 

Pratt Institute, Brooklyn, N. Y. 

July, 1923 

























































CONTENTS 


PAGE 

CHAPTER I 

Principles of Roof Framing: —Explanation of Terms—Measure¬ 
ments—Adjustable Pence—-Laying Out—Problems. 15 

CHAPTER II 

How to Frame a Gable Roof: —Specifications—Layout—Rafters. . 31 

CHAPTER III 

How to Frame a Roof of Equal Pitch: —Specifications—Layout — 
Common Rafters—Jack Rafters—Hip Rafters—Valley Rafters— 
Runs and Lengths of Rafters. 37 

CHAPTER IV 

Seven Problems for Practice in Framing Roofs of Equal 
Pitch:— Tables of Runs and Lengths of Rafters Used in 
Framing Each Problem. 59 

CHAPTER V 

How to Frame a Roof of Unequal Pitch . 127 

CHAPTER VI 

An Advanced Problem in Framing an Unequal Pitch Roof 
with Dormers: —Problem 8 —With Tables of Runs and Lengths 
of Rafters. 164 


7 







s 


CONTENTS 


PAGE 

CHAPTER VII 

How to Frame a Gambrel Roof . 191 

CHAPTER VIII 

How to Determine the Lengths of Roof Rafters. 215 

CHAPTER IX 

How to Frame a Curved Rafter Roof. 222 

CHAPTER X 

How to Frame a Conic Roof .237 

CHAPTER XI 

How to Develop Hopper Bevels . 246 

CHAPTER XII 

How to Miter Rake and Level Mouldings. 253 

Questions for Review. 258 

Index . 261 










LIST OF ILLUSTRATIONS 


FIGURE 


PAGE 


1 Fundamental Lines. 

2 Roof Pitches and Degrees. 

3 Roof Plan Showing Hip, Valley, Common, Jack and 

Cripple Rafters . 

4 Full Size Section Showing the Various Deductions to Be 

Made Where Rafters Intersect Another Rafter. 

5 The Adjustable Fence. 

6 Applying the Fence and Scpiare to a Rafter. 

7 Plan of Gable Roof. Also Elevation of a Rafter on the 

Plan, Showing Method of Determining the Height of 
the Plate . 

8 Developed Length of a Common Rafter. 

0 Elevation of a Gable Roof, Showing Method of Assembling 

the Rafters . 

10 Plan of Hip and Valley Roof of Equal Pitch, from Which 

the Working Layout Is Made. 

11 Developed Length of Common Rafter No. 4. 

12 Developed Length of Jack Rafters, Nos. 1, 2 and 3. 

13 Developed Length of Jack Rafters, Nos. 5, 6 and 7. 

14 Developed Length of the Hip Rafter. 

15 Using a Try Square as an Accessory to the Steel Square to 

Lay Off Part of a Foot Run. 

16 Developed Length of the Valley Rafter. 

17 Showing the Intersection of the Hip and Valley Rafter 

and the Ridge. 

18 Elevation of Hip Roof of Equal Pitch, Showing Method 

of Framing the Rafters. 

19 Graphic Method of Developing the Lengths and Bevels 

of the Various Rafters Used in Framing an Equal- 

Pitch Roof . 

20 Plan of Problem No. 1, from Which the Working Layout 

Is Made . 

21 Section Through Ridge G, Showing a Method of Determin¬ 

ing the Length of the Ridge. 


16 

17 

20 


24 

27 


32 

34 

35 


38 

40 

42 

44 

46 

48 

51 

53 

54 


56 


63 


64 


9 























10 


LTST OF ILLUSTRATIONS 


FIGURE PAGE 


22 Section Through Ridge H, Showing a Method for Determin¬ 

ing the Length of the Ridge and for Fitting into the 
Valleys B and D. 65 

23 Developed Length of Hip A. 67 

24 Developed Length of Hip E. 69 

25 Front and Right Side Elevation, Problem 1, Showing 

Method of Framing the Rafters. 70 

26 Rear and Left Side Elevation, Problem 1, Showing Method 

of Framing the Rafters. 71 

27 Plan of Problem No 2, from Which the Working Layout 

Is Made . 74 

28 Front and Right Side Elevation, Problem 2, Showing the 

Method of Framing the Rafters... 75 

29 Rear and Left Side Elevation, Problem 2, Showing the 

Method of Framing the Rafters. 76 

30 Plan of Problem 3, from Which the Working Layout 

Is Made . 79 

31 Front and Right Side Elevation, Problem 3, Showing the 

Method of Framing the Rafters. 80 

32 Rear and Left Side Elevation, Problem 3, Showing the 

Method of Framing the Rafters. 80 

33 Plan of Problem 4, from Which the Working Layout 

Is Made . 82 

34 Front and Right Side Elevation, Problem 4, Showing the 

Method of Framing the Rafters. 83 

35 Rear and Left Side Elevation, Problem 4, Showing the 

Method of Framing the Rafters. 84 

36 Plan of Problem 5, from Which the Working Layout 

Is Made . 88 

37 Front and Right Side Elevation, Problem 5, Showing the 

Method of Framing the Rafters. 89 

38 Rear and Left Side Elevation, Problem 5, Showing the 

Method of Framing the Rafters. 00 

39 Plan of Problem 6, from Which the Working Layout 

Is Made . 03 

40 Section Through Dormer, Problem 6. Showing a Method 

of Determining the Height of the Dormer Plate Above 
the Main Plate of the Building. 04 





















LIST OF ILLUSTRATIONS 


11 


FIGURE PAGE 


41 Front and Right Side Elevation, Problem 6, Showing the 

Method of Framing the Rafters.*. 95 

42 Rear and Left Side Elevation, Problem 6, Showing the 

Method of Framing the Rafters. 96 

43 Plan of Problem 7, from Which the Working Layout 

Is Made . 101 

44 Section Through Valley D, Figure 43. 103 

45 Developed Length of Valley D. 104 

46 Section Through Hips E, F and G and Ridge P, Figure 43, 

Showing a Method of Framing the Rafters Together.... 106 

47 Developed Length of Hip E. 107 

48 Section Through E, F and G, Figure 43, Showing Inter¬ 

section of Plate and Facia Lines. 109 

49 Developed Length of Hip F. Ill 

50 Section Through Hip I and Valley J, Figure 43. 114 

51 Developed Length of Hip 1. 116 

52 Developed Length of Valley J. 119 

53 Front and Right Side Elevation, Problem 7, Showing the 

Method of Framing the Rafters. 121 

54 Rear and Left Side Elevation, Problem 7, Showing the 

Method of Framing the Rafters. 121 

55 Plan of Hip and Valley Roof of Unequal Pitch, from Which 

the Working Layout Is Made. 129 

56 Common Rafters Developed on the Plan. With the Pitch, 

Projection, Width of Facia and Plancher Levels Known, 
the Heights of the Plates Can Be Determined. 130 

57 Developed Length of Long Common Rafter No. 16. 132 

58 Developed Length of Jack Rafters Nos. 12, 13, 14 and 15.... 133 

59 Full Size Section Through W-W Figure 55, Showing Inter¬ 

section of Jack and Hip Rafters on the Long Common 
Side . 134 

60 Developed Length of Jack Rafters Nos. 17, 18, 19 and 20. ... 136 

61 Developed Length of Short Common Rafter No. 6. 139 

62 Developed Length of Jack Rafters Nos. 1, 2, 3, 4 and 5. 141 

63 Full Size Section Through U-U, Figure 55, Showing Inter¬ 

section of Jack and Hip Rafters on the Short Common 
Side . 

64 Developed Length of Jack Rafters Nos. 7, 8, 9, 10 and 11... 144 

65 Developed Length of Hip Rafter. 147 























12 


LIST OF ILLUSTRATIONS 


FIGURE PAGE 

66 Full Size Section Through R-R, Figure 55, Showing Inter¬ 

section of the Hip Rafter Plate and Facia Line. 148 

67 A Simple Method of Finding the Rise in Inches Per Foot 


of Run . 

68 Developed Length of the Valley Rafter. 154 

69 Full Size Section Through S-S, Figure 55, Showing Inter¬ 

section of the Valley Rafter, Plate and Facia Line. 155 

70 Full Size Section Through V-V, Figure 55, Showing Inter¬ 

section of the Hip and Valley Rafters and the Ridge.... 157 

71 Elevation of Unequal Pitch Roof, Showing Method of 

Framing the Rafters . 158 

72 Graphic Method of Developing the Lengths and Bevels of 

the Various Rafters Used in Framing an Unequal 
Pitch Roof . 160 

73 Plan of Problem 8, from Which the Working Layout Is 

Made . 165 

74 Developed Length of Common Rafter No. 7. 167 

75 Developed Length of Jack Rafter No. 4. 168 

76 Developed Length of Cripple Rafter No. 30. 170 

77 Developed Length of Hip Rafter A . 172 

78 Dormer W, Showing Method of Determining the Dormer 

Plate Level . 175 

79 Dormer S, Showing Method of Determining the Dormer 

Plate Level . 176 

80 Dormer T, Showing Method of Determining Dormer Plate 

Level . 178 

81 Dormer U, Showing the Method of Determining the Dormer 

Plate Level and the Position of Valley G. 180 

82 Developed Length of Valley G. 183 

83 Intersection of Ridge N, Hip F and Valley G and Valley 

G and Header Q. 184 

84 Front and Right Side Elevation of Problem 8, Showing 

the Method of Framing the Rafters. 185 

85 Rear and Left Side Elevation of Problem 8, Showing the 

Method of Framing the Rafters. 186 


87 End View, Showing Method of Developing Profiles of the 
Common Rafters. With the Pitch, Projection, Width of 
Facia and Plancher Level Known, the Plate Level Can 
Be Determined . 194 






















LIST OF ILLUSTRATIONS 


13 


FIGURE PAGE 


88 Graphic Method for Laying Out the Pitch of the Common 

Rafters at 30 and 60 Degree Angles. 195 

89 Developed Length of Lower Common Rafter No. 5. 198 

90 Developed Length of Lower Jack Rafters Nos. 6, 7 and 8... 200 

91 Developed Length of Lower Valley Rafters B. 201 

92 Developed Length of Upper Common Rafters No. 1. 207 

93 Developed Length of Upper Jack Rafters Nos. 2, 3 and 4.... 203 

94 Developed Length of Upper Valley Rafters A. 210 

95 Elevation of Gambrel Roof, Showing Method of Framing 

Rafters . 212 

96 Diagram for Obtaining Lengths of Common, Jack and 

Cripple Rafters . 216 

97 Diagram for Obtaining Lengths of Hip and Valley Rafters.. 218 

98 Diagram for Obtaining Lengths of Hip and Valley Rafters.. 220 

99 Plan of Curved Rafter Roof, from Which the Working Lay¬ 

out Is Made . 223 

100 The Profile of a Common Rafter Developed on the Plan. 

The Hip Rafter Is Developed from the Profile of the 
Common Rafter . 227 

101 Developed Length of a Hip Rafter, Showing Method of 

Transferring Lines from the Layout to the Rafter Stock.. 229 

102 Enlarged Section Through S-S, Figure 99, Showing the 

Amount of Backing for the Hip Rafters. 232 

103 Developed Length of Jack Rafters. 234 

104 Enlarged Section Through S-S, Figure 99, Showing the 

Intersection of the Hip Rafter. Also Enlarged Section 
Through W-W, Figure 99, Showing Intersection of Hip 
and Jack Rafters. 235 

105 Elevation of Curved Rafter Roof, Showing the Method 

of Framing . 236 

106 Plan of Conic Roof, from Which the Working Layout Is 

Made . 238 

107 (1) Details of Finial. (2) Enlarged Section Showing 

Method of Intersecting the Rafters. (3) Developed 
Upper End of Rafters B, Showing Method of Fitting 
Them Against the Sides of Rafter A. 239 

108 Elevation of Conic Roof, Showing Method of Framing. 242 

109 Elevation of Conic Roof, Showing Method of Sheathing. 244 



















14 


LIST OF ILLUSTRATIONS 


PAGE 


110 Assembled Hoppers, the One on the Left Showing a 

Miter Joint; the One on the Right a Butt Joint. 246 

111 Graphic and Steel Square Method for Determining a 

Miter Joint for a Hopper. 247 

112 Graphic and Steel Square Method for Determining a Butt 

Joint for a Hopper. 250 

113 Method for Developing the Profile or Outline of Rake and 

Level Mouldings, so That the Various Members Will 
Intersect When Mitered. 254 

114 Making Plumb Cut on Rake Moulding in Miter Box, and 

Illustrating the Assembled Mouldings. 255 

115 Miter Box, Showing Graphic Method for Laying Out Top 

Cut for Rake Moulding. 256 

116 Miter Box, Showing Method for Determining Side and Top 

Cuts for Rake Moulding. 257 









A PRACTICAL COURSE IN 
ROOF FRAMING 


CHAPTER I 

PRINCIPLES OF ROOF FRAMING 

The simplest and quickest way of framing a roof 
in a practical manner is with the steel square. Roof 
framing is one of the most difficult problems with 
which the carpenter has to deal; not because of the 
number of complicated details, for there are few of 
these involved, but because of his inability to apply 
certain fundamental principles in laying out the dif¬ 
ferent bevels which must be cut in order to make the 
rafters frame into one another correctly. 

Roof Framing Terms .—Before proceeding to consider 
the principles upon which a system of framing should 
be developed, the reader must familiarize himself with 
the terms used in framing a roof. They must be care¬ 
fully studied and understood and thoroughly fixed in 
the mind before attempting to use the square. 

Lines .—There are onlv three lines to be considered; 
a level line, a plumb line and a diagonal line. With the 
proper application of these three lines, all the neces¬ 
sary cuts may be obtained for framing the most com¬ 
plicated roof. 

15 


0 




16 


COURSE IN ROOF FRAMING 


Run .—A horizontal line under the rafter. A level 
line, Figure 1, extending from the outer edge of the 
facia to a plumb line from the center of the ridge. 
The total run of a rafter is one-half the span of the 
building plus one projection. 



* 

Rise .—A perpendicular line from the top of the 
facia line to the top of the ridge end of the rafters. 
A plumb line, Figure 1. 

Pitch .—The slant of the rafters represented in inches 
to the foot. A diagonal line, the diagonal of the run 
and rise, Figure 1. Pitches are spoken of as 1/4, 1/3 


























PRINCIPLES OF ROOF FRAMING 


17 




i i i v i i i —i—i—i r I i i 

16 15 14 13 It II 10 9 8 7 6 5 4 3 Z I 


in 

in 

Q3 

<u 

QJ> 

1 


*- 

O' 

<u 

Cl. 


1 

63 ! 

23 

24 

62 ! 

11 

12 

61 ! 

7 

A 

60 ! 

5 

fc 

59 

■ 9 
24 

571 

3 

4 

56 ! 

17 

24 

54 ! 

2 

3 

53 ! 

5 

T 

51 ! 

7 

12 

49 ! 

13 

24 

47 ! 

1 

2 

45 

11 

24 

42 ! 

5 

12 

40 

3 

8 

37 

► 

3 

33 ! 

7 

24 

30 ! 

i 

4 

26 ! 

5 

24 

22 ! 

1 

6 

-lev* 

oo 

1 

8 

14 

i 

12 

9 ! 

1 

24 

4 ! 


Figure 2.—Roof Pitches and Degrees 










18 


COURSE IN ROOF FRAMING 


or 1/2 pitcli as shown in Figure 2. If the total run of 
a rafter is one-half the span of the building plus one 
projection, a rafter with a total rise equal to the total 
run would be one-half pitch. In a full pitch roof, the 
total rise of the rafters would be equal to the span of 
the building plus the projection on either side or twice 
the distance of the run. In Figure 2 are shown all 
pitches from a rise of one inch to the foot up to twenty- 
four inches to the foot. 

Span .—The width of the building; the distance from 
Avail line to wall line. 

Rake .—The rake of a roof is its pitch or slope from 
the ridge to the eaves. 

Plate Level .—The height of the walls of the building, 
Figure 1, is determined by the pitch of the rafter. 

Plancher Level .—The height of the plancher level 
must be taken from an elevation plan of the building. 
It varies with each job according to the desire of the 
architect. Figure 1. 

Plancher. — The plancher is the covering or ceiling 
that closes up the underside of that part of the roof 
which projects beyond the Avails, forming the projection 
or eaves which shed the Avater that falls upon the roof. 

Birdsmouth .—A notch cut in the rafter to fit over 
the plate. Figure 1. A seat cut for overhanging rafters 
to rest on the plate. The size of the birdsmouth is a 
matter of individual judgment. A good bearing must 
be had on the plate without weakening the rafter too 
much. 

The plancher level, projection, width of facia and 
pitch of the roof is given by the architect. With this 




PRINCIPLES OF ROOF FRAMING 


19 


information the plate level can be determined as shown 
in the illustration. 

Projection. —The distance from the wall line to the 
facia line when rafters overhang the building. It forms 
the eaves or cornice and sheds the water away from 
the building. Figure 1. 

Wall Line. —This is the building line. Figure 1.— 
The outer framework or walls of the building. 

Facia Line. —The inside of the facia forming the 
cornice. Figure 1. 

Ridge. —Stock about one inch thick inserted between 
the rafters at the top. The ridge should be wide enough 
to receive the whole depth of the rafter and should ex¬ 
tend the entire length of the roof. It serves to keep 
the rafters from falling sideways and holds the roof 
frame in place until the roof boarding is on. Figure 1. 

Common Rafters. —Rafters which extend clear up 
from the plate to the ridge and are not connected with 
any of the other rafters. Figure 3. 

Jack Rafters. —Rafters shorter than common rafters 
and which do not extend from the plate to the ridge, 
but are connected at one end to a hip or valley rafter. 
Figure 3. 

Cripple Rafters .—Rafters that are connected at both 
ends to a hip or valley rafter without having a bearing 
on the plate or ridge. Figure 3. 

Valley Rafters. —Rafters that are needed at every 
corner between the main building and an ell or other 
projection. Figure 3. 

Hip Rafters. —The rafters found at every outside 
corner. Opposite of valley rafters. Figure 3. 





20 


COURSE IN ROOF FRAMING 


Measurements .—The top edge of the roof timbers 
must be in alignment to receive the roof boards or fur¬ 
ring strips. Generally it is not essential that the bottom 
edge of the rafters be kept in line. Very often an 



Figure 3.—Roof Plan Showing Hip, Valley, Common, Jack and Cripple 

Rafters 

attic is left unfinished and in case it is to be finished 
the ceiling can usually be straightened enough at the 
time the plaster is put on. There is always sure to 
be some variation in the widths of the timbers unless 










































































PRINCIPLES OF ROOF FRAMING 


21 


they have been previously sized to a uniform width. 
This is seldom done unless the rafters are to be ex¬ 
posed to view to give some desired architectural effect. 
If the top edges of the timbers are to be brought into 
alignment, then it is obvious that some definite point 
on the rafters must be selected from which to compute 
the required measurements. The top edge of the rafter 
then becomes the face or working edge. 

To locate the exact position of the rafter, refer to 
Figure 3. A roof plan shows only center lines of the 
rafters and ridges. A line, being without breadth or 
thickness, gives a very definite location. The length 
of a rafter developed from a. run measured on a center 
line will fit only over the particular line on which the 
run was measured. 

Then again, all measurements are taken on a level 
or a plumb line. The plan of a roof is a view looking 
from above, which gives the appearance of the roof 
laid flat or level. In order to apply these lines they 
must be applied in a relative position or on a level line. 
There is always a great temptation to pick the lines up 
from the plan and apply them to the top edge of a 
rafter, which, in its relative position, forms the slant 
or pitch of the roof. Therefore, all measurements must 
be taken on a level or plumb line on the center line of 
the rafter and from the top edge. 

For example, in laying off the width of the facias; 
measure down on the facia line, a plumb line, from the 
top edge of the rafter, the required width of the facia, 
thus locating the plancher level. To locate the wall 
line, measure on a level line, from the facia line, the 


Facia Line 


22 


COURSE IN ROOF FRAMING 






Figure 4. Full Size Section Showing the Various Deductions to Be 
Made Where Rafters Intersect Another Rafter 











































PRINCIPLES OF ROOF FRAMING 


23 


required width of the projection, producing a plumb 
line parallel to the facia line and the width of the pro¬ 
jection away, giving the wall or building line. If the 
lines on the plan represent center lines, the lengths ob¬ 
tained with the steel square are extreme lengths oil 
these center lines. 

To obtain the cutting length of the rafters certain 
deductions must be made from these lengths where 
rafters intersect each other. Where a ridge intersects 
another ridge at right angles deduct one-half the thick¬ 
ness of the ridge, A-B, Figure 4 -D. Where a hip or val¬ 
ley rafter intersects a ridge deduct one-lialf the diagonal 
thickness or one-half the thickness of the hip or valley 
measured on the line of the ridge, G-H, Figure 4 -D. 
Where a jack rafter intersects a hip or valley deduct 
one-half the diagonal thickness or one-half the thickness 
of the hip or valley rafter measured on the line of 
the jack rafter, C-D, Figure 4-A. Where a hip or valley 
rafter intersects another hip or valley at right angles 
deduct one-half the thickness of the hip or valley, E-F, 
Figure 4 -B. Where a hip or valley rafter intersects a 
ridge deduct one-half the diagonal thickness or one- 
lialf the thickness of the ridge measured on the line 
of the hip or valley, 1-J , Figure 4-C. After making these 
deductions, square the plumb line across the top edge 
and locate the center point. Through this center point 
lay out the necessary top cut. 

Adjustable Fence .—A necessary accessory to the 
steel square in laying out a rafter is an adjustable 
fence as shown in Figure 5. This fence is made from 
a piece of black walnut, birch or cherry, %" thick, about 


24 


COURSE IN ROOF FRAMING 



Figure 5.—The Adjustable Fence 









PRINCIPLES OF ROOF FRAMING 


2 5 


IY 2 " wide and 24" long. Run a saw kerf down the cen¬ 
ter of the fence as shown at A, cutting the fence about 
9" from each end and leaving about 6" of solid wood in 
the center. Bore a series of holes about in diam¬ 
eter and 1" apart as shown at B. 

Insert the blade of the square in the saw kerf at 
one end of the fence and the tongue in the kerf at 
the other end, the fence then forming the third side 
of a right-angled triangle, and the blade and the tongue 
of the square forming the other two sides. The fence 
is held tightly on the square by two round headed stove 
bolts as shown at C. A washer is placed under the 
head as well as under the nut to prevent the screw from 
sinking into the stock. 

Application of the Fence .—In Figure 5 the fence is 
adjusted to lay out a rafter with a 5/12 pitch; that is, 
a rise of 10" to the foot. 

Place the fence so that it rests on the 12" mark on 
the blade as at E and at 10" on the tongue as at D. 
Tighten the screws to hold the fence in position while 
applying it to the stock. 

All rafters rise so many inches in one foot, therefore 
the 12" mark on the blade is the unit to be used in 
laving out all common rafters and remains the same 
for all roofs of equal pitch. The rise per foot varies 
according to the desire of the owner of a building or 
the ideas of an architect so that the rise, or figure on 
the tongue, may vary with every new roof. However, 
with the rise once determined, it remains fixed for the 
laying out of all common rafters for that particular 
roof. 


26 


COURSE IN ROOF FRAMING 


The distance from D to E, Figure 5, is the length of 
the rafter for one foot of run. All measurements must 
he taken on the outside of the fence as shown. The 
run, a level line, a unit of 12", and usually the longest 
distance, should be laid off on the blade, while the rise, 
which is a plumb line changing with the construction of 
each roof, and usually the shorter distance, is laid off 
on the tongue. If this rule is followed and practiced a 
mechanic cannot substitute the rise for the run or 
become confused in laying out his rafters. 

The fence is applied to the rafter as shown in Figure 
6. With the top edge of the rafter toward the operator, 
slide the square to the extreme right, thus producing 
the first plumb cut or facia line. The successful com¬ 
pletion of the work depends upon the accuracy of the 
operator in adjusting the fence and of applying it to 
the stock. A variation in the distance D to E, Figure 5, 
which is the length of one foot run, may make a con¬ 
siderable difference when applied ten or twelve times 
for a rafter whose run is 12'0". 

In Figure 6 rafters are being laid out whose run 
is 4'0". After producing the facia line, hold the square 
firmly and slide it to the extreme left until the 12" 
mark on the blade coincides with the facia line on the 
top edge of the rafter. Then mark on the left hand 
side of the square or tongue, repeating this operation 
four times, marking the extreme ends to be cut and 
thus giving the length of the rafter for a run of 4'0" 
rising at an angle of 10" to the foot. 

With the pitch of the roof determined, all lines are 
parallel to each other; that is, after producing the facia 


PRINCIPLES OP ROOF FRAMING 


27 


line the wall line must be parallel to it and after pro¬ 
ducing the plancher level, the plate level must be parallel 
to it. 

Laying Out .—The importance of making layouts can¬ 
not be over emphasized. They are labor savers as well 
as material savers and they serve as a constant check 



Figure 6.—Applying the Fence and Square to a Rafter 


which tends to prevent errors. Layouts, generally 
speaking, are full size drawings showing complete de¬ 
tails of construction. They are different from archi¬ 
tects’ drawings, which are usually more of a design 
than a working drawing. Mechanics put the architects’ 
ideas into conventional form and help to carry out these 
ideas as far as it is practical for them to do so. 













28 


COURSE IN ROOF FRAMING 


Layouts are shop drawings from the viewpoint of 
a mechanic; showing all the intersecting parts of a 
job and giving height, width and thickness, from which 
can he itemized complete stock lists of material showing 
the exact number of pieces required and their actual 
finished dimensions. Various sections of a job can 
be carried on simultaneously by different groups of 
men with the assurance that the various parts, when 
assembled as a whole, will fit perfectly. 

The first step in framing a roof of any description is 
to make a layout. If the roof is a simple one, such as 
a plain gable, a freehand sketch is all that would be 
required. If a roof is at all irregular a layout should 
be made to scale. Whenever possible layouts should 
be made full size. 

In laying out a roof it would be impractical to lay 
it out full size, so a convenient scale is selected. The 
author usuallv uses a 1" scale, so that when measure- 
ments are picked up from the layout they are called 
feet instead of inches. That is, every distance taken 
from the layout would he twelve times as long full size. 
A measurement 4" long on the layout would read 4'0" 
and a measurement 14^" long on the layout would read 
14 y 2 feet or 14'6" actual measurement. It is a very 
convenient scale and one that requires few calculations. 

Center lines of the various rafters are the only 
lines used on the layout. It is on these lines that the 
runs of the rafters are measured, thus giving a definite 
location irrespective of any variation in the sizes of 
the roof timbers used. The rafters will fit only over 
the center lines on which the run of the rafters is 


PRINCIPLES OP ROOF FRAMING 


29 


measured except in places where a number of common 
rafters are the same length. 

Great care should be exercised in making* a layout. 
It should be accurate in every detail. The least varia¬ 
tion in laying out a job will be greatly magnified in 
picking up the runs of the rafters. The facia and wall 
lines should be parallel with each other. The return 
facia and wall lines should be at right angles with each 
other. The hip and valley rafters should cross the plate 
at an angle of forty-five degrees. The jack rafters 
should be square with the plate and the ridges should 
be parallel with the facia lines. The rafter lines should 
be numbered consecutively and the corresponding num¬ 
bers put on the rafters as they are laid out. If this 
plan is followed considerable time will be saved in 
sorting out the rafters. The roof can be framed before 
the walls are up with the assurance that every rafter 
will fit the location for whjph it was intended. If need 
be, the timbers and layout can be passed on to another 
group of men to assemble without experiencing any 
difficulty in locating the proper place for each and 
every rafter. 

Problems for Practice .—Satisfactory results in learn¬ 
ing how to frame a roof can best be obtained by actually 
framing a roof. To many mechanics it is a puzzle and 
the only way to master the subject is to work at the 
puzzle until it is solved. The text makes suggestions of 
suitable sizes of stock that may be used in framing 
the problems and urges and encourages readers to 
practice the application of the principles described. 
The problems are carefully selected and offer excellent 



30 


COURSE IN ROOF FRAMING 


material for practice in laving* out and framing com¬ 
plete roofs. They afford an opportunity for individual 
study that is not possible in the industry, and if prop¬ 
erly studied, they will greatly reduce the time usually 
spent in the trade in acquiring similar information. 

An effort has been made to standardize the use of 
reference letters so that similar lines and positions 
throughout the text are represented by the same letter 
which greatly facilitates following the text. The im¬ 
portant lines are represented by the following letters: 

A —facia line. 

B —wall line. 

C —extreme length of rafters on the center line. 

D —cutting length of the rafters on the center line. 

F —plancher level. 

G —plate level. 

1 — cheek cut. 

2 — top cut. 

The dimensions given on the plans are in inches 
so that the layouts and problems can be made full size. 
To apply full size, read inches as feet. The runs should 
be taken from the layouts and the lengths of the rafters 
developed with the steel square and fence. To aid the 
student in checking up his work, a table giving the 
runs and lengths of all rafters will be found immediately 
following each problem. 



CHAPTER II 


HOW TO FRAME A GABLE ROOF 

A gable roof is a ridged roof the end of which is not 
hipped but cut off in a vertical plane; as the end wall 
of a building. It is the most common roof of all, very 
simple in form and easy to construct. 

Specifications. —Plate, %" x 2 1 4". 

Rafters, %" x 

Ridge, %" x 1 y 8 ". 

Projection, 2 yS'. 

Facia, %". 

Plancher level to plate level, 2%". 

Pitch, 10" rise in 1 foot (5/12 pitch). 

Dimensions (see plan.) Figure 7. 

Rafters spaced 2" on centers. 

Layout .—It will be unnecessary to make a layout of 
the gable roof as suggested for the succeeding prob¬ 
lems. The rafters are all the same length, the run 
being one-lialf the span plus the projection. It will be 
necessary to determine the height of the walls or plate. 
In all the problems in the text the distance between 
plancher level and plate level is mentioned in the speci¬ 
fications. This distance is not fixed but rests upon the 
judgment of each individual mechanic. 

The reader should have a clear understanding at this 
point of how these measurements are determined. With 
the pitch, projection, plancher level and width of facia 
given by the architect or owner, the height of the wails 

31 


32 


COURSE IN ROOF FRAMING 


or plate level can be determined. The architect gives 
the lines of the building that are seen. The framer 
determines the lines that are not seen. 



Figure 7.—Plan of Gable Roof. Also Elevation of a Rafter on the 
Plan, Showing Method of Determining the Height of the Plate 


To determine the location and size of the birdsmouth 
draw in the profile of one common rafter on the plan 
as shown in Figure 7. Draw in the top edge of the 
rafter first, at a pitch, rising 10" in one foot. Produce 






































































































HOW TO FRAME A GABLE ROOF 33 

the first plumb line to the extreme left, A, Figure 7, 
for the facia line. Then measure in on a level line 
the width of the projection, 214", and produce wall 
line B. Measure down on facia line A from the top 
edge of the rafter the width of the facia, and pro¬ 
duce planclier level F. In laying out the birdsmouth, 
care should be taken not to weaken the rafter, yet to 
have a good seat cut. The author has found that a 
plate level located in the center of the rafter on the 
wall line or plumb line B gives a nicely proportioned 
birdsmouth. 

Locate the center of the rafter on wall line B and 
produce a level line, giving plate level G. Measure on 
a plumb line the distance between planclier level F 
and plate level G, which will be found to be 2%" as 
given in the specifications. When this distance is once 
determined all rafters are cut alike due to the fact that 
the planclier is level and the plate is level throughout 
the building, so that this measurement remains constant 
when once determined and applies to hips and valleys 
as well as to common rafters. 

To Lay Out the Common Rafter .—Set the fence and 
square at 10" rise on the tongue and 12" run on the 
blade. Mark on the tongue for all plumb cuts and on 
the blade for all level cuts. Press the fence firmly 
against the top edge of the stock to be used for the 
rafter and produce the facia line or the first plumb line 
to the extreme left, A, Figure 8. Slide the square to 
the right until the 12" mark on the blade coincides with 
the facia line and the top edge of the rafter. Mark 
on the tongue for the length of one foot run as shown 



34 


COURSE IN ROOF FRAMING 


by dotted line S. The total run required is 12%", one- 
lialf the span of the building plus the projection. Slide 
the square again to the right and measure on a level 
from plumb line S the remaining run of the rafter, 
making a total run of 12%". Then produce plumb line 



Figure 8.—Developed Length of a Common Rafter 


C, the extreme length to the center line of the ridge. 
From this length deduct one-half the thickness of the 
ridge, 3/16", and produce plumb line D , the cutting 
length of the rafter. Measure in from facia line A , on 
a level line, 2%", the width of the projection and pro¬ 
duce wall line B. Measure down on facia line A from 





























HOW TO FRAME A GABLE ROOF 


35 


the top edge of the rafter, the width of the facia 
and produce plancher level F. Measure up from 
planclier level F , on a plumb line, 2 1 /s", locating plate level 



Figure 9.—Elevation of a Gable Roof, Showing Method of Assembling 

the Rafters 


G. Cut on line A for the facia, on line F for the plancher 
level, on lines B and G for the birdsmoutli and on line 
D for the ridge cut. The length of the ridge is the en¬ 
tire length of the roof, 28". 





36 


COURSE IN ROOF FRAMING 


Runs and Lengths of Rafters .—The following table is 
prepared to assist the student in checking up his work. 
It is intended that the framer will take his runs from 
the plan and develop the length of the rafters with the 
steel square and fence, using the table only as a matter 
of information giving him assurance that he has taken 
the proper run and determined the correct length of the 
rafters before cutting his stock. The measurements 
listed in the table are extreme lengths on the center 
lines. Where rafters intersect the ridge make allow¬ 
ance for the cutting length. It is suggested that the 
student make a model of the roof for practice, building 
it to 1" scale. In using the table, read feet as inches. 
For example, the run would read 12%" and the 
3V " 

74 The square being laid out in twelfths 


length 16 


12 


of an inch, it is an easy matter to check up the work 
accurately. 


RUNS AND LENGTHS OF RAFTERS USED IN FRAMING GABLE 



ROOF- 

-5/12 PITCH 


Quantity of 
Rafters 

Run 

Lengths | 

Kind of Rafters 

30 

12'6" 

16'31/U' 

Common Rafters 

1 

2 8'0" 

2 S'O" 

Ridge 


Figures used on the steel square—10" on tongue, 12" 
on blade. Mark on the tongue for plumb cuts and on 
the blade for level cuts. 











CHAPTER III 


HOW TO FRAME A ROOF OF EQUAL PITCH 

An equal pitch roof is one in which all rafters 
throughout the entire roof are at the same slant or 
pitch. All hip and valley rafters cross the plate at an 
angle of forty-five degrees. The jack rafters cross the 
plate at right angles, the center lines of which, inter¬ 
secting with the center lines of the hip and valley 
rafters, form a perfect square with the facia line, the 
center lines of the hip and valley rafters running the 
diagonal of a square. 

Specifications .—Plate %" x 2". 

Hip and valley rafters, %" x 114 ". 

Common and jack rafters, %" x 

Ridge, %" x 1%". 

Projection, 1V>". 

Facia, 

Planclier level to plate level, 1%". 

Pitch, 9" rise in one foot (%" pitch). 

Dimensions (see plan, Figure 10). 

Rafters spaced 2" on centers. 

Layout .—A full size working layout of the plan, 
Figure 10, should be drawn on a hoard or a sheet of 
detail paper. The layout will represent a scale of 1" 
to the foot. In applying the various measurements full 
size, substitute the word feet for inches in listing the 
runs and lengths of the various rafters. Number each 

rafter and ridge as shown on the plan. Put the cor- 

37 


38 


COURSE IN ROOF FRAMING 


responding* number on the rafters as they are laid out 
to insure ready identification and proper location dur¬ 
ing the erection of the roof. 

It will also be necessary to develop a profile of a 
common rafter on the layout, similar to that shown 
in Figure 7, to determine the proper heights of the walls. 



Figure 10.—Plan of Hip and Valley Roof of Equal Pitch, from Which 

the Working Layout Is Made 

There is no fixed rule for determining the distance 
from the plancher level to the plate level. The architect 
gives the pitch of the roof, the projection, the width 
of facia and the plancher level, the lines of the roof 
that are seen. The framer must develop the lines that 
are not seen or the plate levels. 

























































HOW TO FRAME A ROOF OF EQUAL PITCH 


39 


In laying out the birdsmouth care should be taken to 
have a good seat cut and yet not to weaken the rafter 
at this point. Lay in the top edge of the rafter to 
the pitch desired, as shown in Figure 7, and a second 
line parallel to it, a distance apart equal to the width 
of the stock to be used for the rafters. Measure down 

on the facia line from the top edge of the rafter 

the width of the facia noted in the specifications, and 

produce plancher level F. Measure in on a level line 

from the facia line, the width of the projection, 
and produce the wall line B. In laying out the birds¬ 
mouth the author has found that if the plate level is 
located about in the center of the wall line on the side 
of the rafter it generally works out in good proportion. 

Locate the center of the rafter on wall line B , Figure 
7, and produce plate level G. Measure the distance be¬ 
tween plate level and plancher level and note the dis¬ 
tance in the specifications, Id/j". The plancher level 
and plate levels are level throughout the entire build¬ 
ing so that this distance will remain constant for the 

entire roof. 

To Lay Out the Common Rafters .—The pitch of com¬ 
mon rafters No. 4 required by the specifications is 9" 
rise in one foot. The run is taken from the layout, 
Figure 10, measuring from the facia line to the center of 
the ridge, 7%". Set the fence and square at 9" rise on 

the tongue and 12" run on the blade. Mark on the 

tongue for all plumb cuts and on the blade for all level 
cuts. Press the fence firmly against the top edge of 
the stock to be used and produce the facia line or first 
plumb line to the extreme right, A, Figure 11. Slide 



40 


COURSE IN ROOF FRAMING 


tlie fence to the left and measure on a level line from 
facia line A the run of the rafter, 7%", and produce 
plumb line C, the extreme length of the rafter to the 
center line of the ridge. From this length deduct one- 



Figure 11.—Developed Length of Common Rafter No. 4 


half the thickness of the ridge, 3/16", and produce 
plumb line D t the cutting length of the rafter against 
the ridge. 

To complete the layout of the lower end of the 
rafter, measure in from facia line A, measuring on a 
level line, 1%", the width of the projection, locating 



















HOW TO FRAME A ROOF OF EQUAL PITCH 


41 


wall line, B. Measure down on facia line A from the 
top edge of the rafter, the width of the facia, 

locating plancher level F. Measure up from plancher 
level F, measuring on a plumh line, 1^4", locating plate 
level G. Cut on line A for the facia, on lines G and B 
for the birdsmouth and on line D for the cut against 
the ridge. 

To Lay Out the Jack Rafters .—The lengths of jack 
rafters Nos. 1, 2 and 3 are determined in the same man¬ 
ner as for the preceding common rafters because they 
are a part of the length of them. Take the runs from the 
layout, Figure 10, measuring from the facia line to the 
center of the hip. The three rafters are shown de¬ 
veloped on the side of a single rafter, Figure 12. In 
practice these would be laid out separately hut are 
here laid out one over another to save space and to avoid 
repetition. Press the fence firmly against the top 
edge of the stock to be used and produce the facia line 
or first plumb line to the extreme right A , Figure 12. 
Slide the fence to the left and measure on a level line 
from facia line A the run of rafter No. 1, 2"; the run 
of rafter No. 2, 4"; and the run of rafter No. 3, 6"; 
and produce plumb line C, Figure 12, the extreme 
lengths of the rafters to the center line of the hip 
rafter. From this length deduct one-half the thickness 
of the hip measured on the line of the jack rafters, or 
one-half the diagonal thickness of the hip, full, 

and produce plumb line D on the side of the rafter. 
Square this line across the top edge and locate the 
center point. 

To lay out the top cut so that the jacks will fit against 


42 


COURSE IN ROOF FRAMING 


the side of the hip rafter at the proper angle measure 
forward on a level line from plumb line D a distance 
equal to one-half the thickness of the stock used for the 
jack rafter, 3/16", and produce plumb line 1. Connect 



Figure 12.—Developed Length of Jack Rafters Nos. 1, 2 and 3 


plumb line 1 through plumb line I) on the center line 
as shown at 2, top view, Figure 12. The top cut can 
also be laid out with the steel square by using the 
length, 15" (bridge measure of the run, 12" and the 






























HOW TO FRAME A ROOF OF EQUAL PITCH 


43 


rise, 9") on the blade and the run, 12", on the tongue. 

Mark on the blade for the top cut. 

The lower end of the jack rafters is a duplicate of 
the common rafter. Measure in from facia line A, 
measuring on a level line, 1 y 2 ", the width of the pro¬ 
jection, locating wall line B. Measure down on facia 

line A from the top edge of the rafter, %", the width 

ot the facia, locating plancher level F. Measure up 
from plancher level F, measuring on a plumb line, 
locating plate level G. Cut on line A for the facia, 
on lines G and B for the birdsmoutli and on bevel 2, 
on plumb line 1 for the cheek cut against the hip rafter. 

The lengths of jack rafters Nos. 5, 6 and 7 are de¬ 
termined in the same manner as for the preceding jack 
rafters, the top end of the jacks resting against the 
ridge and the bottom end beveled to fit against the side 
of the valley rafter. Take the runs from the layout, 
Figure 10, measuring from the center of the ridge to 
the center of the valley rafter, Figure 10. The three 
rafters are shown developed on the side of a single 
rafter, Figure 13. In practice these would he laid 

out separately hut are here laid out over one another 

to save space and to avoid repetition. Press the fence 
firmly against the top edge of the stock to be used and 
produce the first plumb line to the extreme left, C, 
Figure 13. Slide the fence to the right and measure 
on a level line the run of rafter No. 5, 6y 2 " ; the run 

of rafter No. 6, ^y 2 "; and the run of rafter No. 7, 2y 2 "; 

and produce plumb line C, Figure 13, the extreme 
length of the jack rafters to the center line of the 
valley rafter. From the top end of the rafter deduct 


44 


COURSE IN ROOF FRAMING 


one-half the thickness of the ridge, 3/16", and produce 
plumb line D, the cutting length of the rafter against 
the ridge. 

The bottom ends of all three rafters are beveled to 



Figure 13.—Developed Length of Jack Rafters, Nos. 5, 6 and 7 


make a fit against the side of the valley rafter. First, 
deduct one-half the thickness of the valley rafter meas¬ 
ured on the line of the jack rafter, or one-half the 
diagonal thickness of the valley, y 2 " full, and produce 





























HOW TO FRAME A ROOF OF EQUAL PITCH 


45 


plumb line D on the side of the rafter. Square this 
line across the top edge and locate the center point. 

To lay out the top cut so that the jacks will tit at 
the proper angle measure back on a level line from 
plumb line D a distance equal to one-half the thickness 
of the stock used for the jack rafters, 3/16", and pro¬ 
duce plumb line 1. Connect plumb line 1 through plumb 
line D on the center line as shown at 2, top view, Figure 
13. The top cut can also be laid out with the steel 
square by using the length, 15" (bridge measure of 
the run, 12", and the rise, 9") on the blade and the 
run, 12", on the tongue. Mark on the blade for the top 
cut. Cut on plumb line D for the cut against the ridge 
and on plumb line 1 and bevel 2 for the cheek cut 
against the valley rafter. 

To Lay Out the Hip Rafter .—Hip and valley rafters 
of an equal pitch roof run diagonally at an angle of 
forty-five degrees with reference to the plates or walls 
of a building. The common rafters run 12" in one 
foot of run, therefore the hip and valley rafters must 
run the diagonal of 12" and 12", or approximately 17". 
In other words, for every foot of run of the common 
rafter the hip rafter runs 1'5". If it does not, then it is 
not an equal pitch roof. The diagonal of 12'0" and 
12'0" is 16'11%", thus losing %" in 12'0". The diagonal 
of 12" and 12" is so near 17" that it can be safely used 
as a constant unit for laying out all hip and valley 
rafters for equal pitch roofs. The rise is the same 
as for the common rafter, 9". The common rafter as 
it rises 9" runs 12", while the hip in rising 9" 
travels 17". 



46 


COURSE IN ROOF FRAMING 


The run of the hip is taken from the layout, Figure 
10, measuring from the facia line to the butt joint 

7 %" 

between the hip and valley rafter, A-T, 10 Set 


the fence and square at 9" rise on the tongue and 17" 
run on the blade. Mark on the tongue for all plumb 
cuts and on the blade for all level cuts. Press the 



fence firmly against the top edge of the stock to be 
used and produce the facia line or first plumb line to 
the extreme left, A, Figure 14. Slide the fence to the 
right and measure on a level line from facia line A, the 

714" 

run of the hip, 10-^-, and produce plumb line T, 
Figure 14, the extreme length of the hip forming the 



















HOW TO FRAME A ROOF OF EQUAL PITCH 


47 


butt joint against the valley rafter. 

To complete the layout of the lower end of the hip, 
measure in on a level line the diagonal distance of 

li/" 

the projection, 1%" and 1%", or 2 - -, locating wall 

line B, Figure 14. Measure down on facia line A from 
the top edge of the rafter %", the width of the facia, 
and produce plancher level F. Measure up from 
planclier level F, on a plumb line, I 14 ", locating plate 
level G, the distance between plate level and plancher 
level being the same for both common and hip rafters. 

To make the return on the facia line at the corner 
of the building measure in on a level line from facia 
line A on the side of the hip a distance equal to one- 
lialf the thickness of the stock used for the hip, %", 
and produce plumb line 1. Square this line across the 
top edge of the rafter. Also square facia line A across 
the top edge and locate the center point. Connect plumb 
line 1 on either side of the hip rafter with the facia 
line on the center line of the hip as shown in the top 
view, 2, Figure 14. 

This top cut can also be laid out with the steel square 
by using 19!/4" (bridge measure of the run 17" and the 
rise 9") on the blade and the run, 17", on the tongue. 
Mark on the blade for the top cut. For convenience 
one-half the run, and one-half the rise, 4 y 2 ", is 

used, giving the bridge measure 9%". 

Short distances can very readily be laid off by using 
a try square in conjunction with the steel square as 
shown in Figure 15. Rest the stock of the try square 
against the outside edge of the steel square and project 



48 


COURSE IN ROOF FRAMING 


the required measurement up from the steel square to 
the stock. The steel square being laid out in twelfths 
of an inch, it is a simple matter to make accurate 
measurements. 

There is always a temptation to measure off the 
level, so that by using the two squares in the manner 
suggested possible errors can be avoided. For ex- 



Figure 15.—Using a Try Square as an Accessory to the Steel Square to 

Lay Off Part of a Foot Run 


fl/" 

ample, to lay off 2- qf -, the diagonal of the projection, 

I 

place the stock of the try square against the top edge 
of the steel square with the outside edge of the blade 

11 /" 

of the try square over the required measurement, 2-—- • 

JLlj 

on the blade of the steel square. Then the blade of the 










HOW TO FRAME A ROOF OF EQUAL PITCH 


49 


11/ " 

try square and tongue of the steel square will be 2-™ 

±z 

apart. With the blade of the try square over the 
facia line, mark on the tongue of the steel square for 
the wall line, which will be exactly parallel to the facia 
li//' 

line 2 — ~ apart. Cut on plumb line 1, on bevel 2 for 


the facia, on line F for the plancher level, on lines G 
and B for the birdsmouth and on line T for the butt 
joint against the valley rafter. 

To Back the Hip Rafter .—It will he necessary to re¬ 
move the corners of the hip rafter to bring the center 
line in alignment with the top edge of the jack and com¬ 
mon rafters. The center lines of both the hip and 
valley rafters seek their natural position when laid out 
with the steel square. Both lines meet at the apex. If 
the hip is dropped or the valley raised it throws the 
center line out of adjustment. If the hip is dropped 
the roof boards will have a bearing only on the outside 
edges of the hip unless blocked up in the center. Back¬ 
ing the hip or removing the corners gives a solid bear¬ 
ing for the roof boards, is better construction than drop¬ 
ping, and keeps the rafters in their normal position. 

To determine the amount of stock to be removed in 
beveling the corners of the hip rafter produce a level 
line anywhere on the side of the rafter as at L, Figure 
14. From the top edge of the rafter, on this level line, 
point off one-half the thickness of the stock used for the 
hip, as at M. Gauge a line • through this point 

parallel to the top edge of the rafter on either side of 
the stock. Also gauge a line through the center on the 




50 


COURSE IN ROOF FRAMING 


top edge. Remove the corner between these two lines 
as shown in the end view, Figure 14. 

To Drop the Hip Rafter .—If it is desired to drop 
the hip rafter to avoid the need for backing, produce a 
level line anywhere on the side of the hip, as at N, 
Figure 14. From the top edge of the rafter on this 
level line, point off one-half the thickness of the stock 
used for the hip, %", as at S. Intsead of gauging a line 
through this point as in backing, erect a perpendicular 
line. The length of this perpendicular line or the dis¬ 
tance R-S, Figure 14, is the amount of stock that 
should be taken off the plate level as shown by the 
dotted line 0, Figure 14. This same amount of stock 
should also be removed from the plancher level as 
shown by the dotted line 0. 

To Lay Out the Valley Rafter .—The length of the 
valley rafter is determined in the same manner as that 
of the preceding hip rafter except that the return on 
the facia line has the reverse cut and the birdsmouth 
differs. Take the run from the layout, Figure 10, 
measuring from the return on the facia line to the butt 

joint against the hip rafter, or 10 . Press the fence 

1 

firmly against the top edge of the stock to be used and 
produce the facia line or first plumb line to the extreme 
right, A, Figure 16. Slide the fence to the left and 
measure on a level line from facia line A the run of the 

valley, 10 - , and produce plumb line T, the extreme 

_L 

length of the rafter forming the butt joint against the 
hip rafter. 





HOW TO FRAME A ROOF OF EQUAL PITCH 


51 


To complete the layout of the lower end of the valley, 
on the side of the rafter measure in on a level line 
the diagonal distance of the projection, 1 y 2 " and 

iy " 

iy 2 ", or from facia line A, locating wall line 77, 

Figure 16. The valley rafter crosses the plate at the 
ell of the building. 



Figure 16.—Developed Length of the Valley Rafter 


To avoid the need for notching the valley to make 
a fit into the corner of the ell, the wall line should be 
moved out, or plumb line B is advanced to plumb line 77, 
Figure 16, a distance equal to one-half the thickness of 
the stock used for the valley, At the corner of the 






















52 


COURSE IN ROOF FRAMING 


building this will leave a hole which is covered over 
with the plancher ceiling. 

To complete the birdsmoutli measure down on facia 
line A from the top edge of the rafter, %", the width 
of the facia and produce plancher level F. Measure up 
from plancher level F, on a plumb line, 1%", locating 
plate level G. 

To make the return on the facia line at the ell of 
the building, measure forward on a level line from facia 
line A a distance equal to one-half the thickness of the 
stock used for the valley, and produce plumb line 1. 
Square plumb line 1 across the top edge of the rafter. 
Also square facia line A across the top edge and locate 
the center point. Connect plumb line 1 on either side of 
the rafter with the facia line at the center as shown 
at 2, top view, Figure 16. This top cut can also be 
laid out with the steel square by using 19%" (bridge 
measure of the run, 17", and the rise 9") on the blade 
and 17" on the tongue. Mark on the blade for the 
top cut. For convenience use one-half the run, 8%", 
and one-half the rise, 4y 2 ", giving the bridge measure 
9%". Cut on plumb line 1, on bevels 2 for the facia line, 
on lines G and H for the birdsmoutli and on line T 
for the butt joint against the hip rafter. The top edge 
of the valley is left square as the corners are not in 
the way for the roof boards since the center line is in 
alignment with the top edge of the common and jack 
rafters. (See end view, Figure 16.) 

To Lay Out the Ridges .—The run of the ridges is 
taken from the layout, Figure 10, both ridges being 
the same length. Measure the extreme length from the 



HOW TO FRAME A ROOF OF EQUAL PITCH 53 

end of the gable to the intersection of the center lines 
of the ridge, hip and valley rafters, or 12 y 2 ". From 
this length deduct one-half the thickness of the hip 



Figure 17.—Showing the Intersection of the Hip and Valley Rafters 

and the Ridge 

measured on the line of the ridge or one-half the diag¬ 
onal thickness of the hip, T-W, Figure 17. Square a 
line across the top edge of the ridge at this point and 












54 


COURSE IN ROOF FRAMING 


locate the center. Through this center point lay out a 
true miter, or angle of forty-five degrees. Cut on this 
bevel, on the top edge, square across the side of the 
ridge. 

To Assemble the Roof .—Assemble the rafters as 
shown in the elevation, Figure 18. Set up and fasten 
the hip and valley rafters first. The center line of 



Figure 18.—Elevation of Hip Roof of Equal Pitch, Showing Method of 

Framing the Rafters 


both rafters must intersect at the apex. Set up the 
ridges next, securing them in place at the proper 
heights with a pair of common rafters. The ridge is 
dropped out of its normal position to prevent the need 
for hacking it, thus throwing the top edge out of 
alignment with the top edge of the hip and valley 





HOW TO FRAME A ROOF OF EQUAL PITCH 


55 


lafteis. Both ridges are oil the same level, but point 
W, Figure 17, is lower than the apex of the roof. 

If the ridges were backed to the pitch of the roof 
and the lines ot the common and jack rafters were con¬ 
tinued to the extreme point, all lines would terminate 
in alignment with the extreme high point formed by 
the intersection of the hip and valley rafters. The roof 
boaids continue these lines up, so that when the roof 
is completed all roof surfaces are in alignment. 

The exact location oi the ridges where they intersect 
the hip and valley rafters may be determined by their 
location with reference to the butt joint of the hip and 
valley rafter. Draw in a section of the hip, valley, 
and ridge, full size, on the layout Figure 10, as shown 
in the section, Figure 17. Square a line across at right 
angles to the center line of the hip and valley rafters 
as at B , Figure 17, thus establishing the butt joint be¬ 
tween the two rafters. The distance B-S gives the 
distance between the butt joint and the long point of 
the bevel of the ridge on the side of the rafter. 

Development of the Bafters on the Plan— Figure 19 
will serve to illustrate and prove the lengths and bevels, 
showing in a graphic way how they are obtained. 

A to B is the rise of the common rafter. 

A to C is the run of the common rafter. 

B to C is the length of the common rafter. 

C to D is the developed length of the common rafter. 

A to E is the rise of the hip and valley rafters. 

A to F is the run of the hip and valley rafters. 

E to F is the length of the hip and valley rafters. 

D to F is the developed length of the hip rafter. 


56 


COURSE IN ROOF FRAMING 


A to T is the developed length of the valley rafter. 
G to II is the developed length of jack rafters No. 1, 
No. 2 and No. 3. 



Figure 19.- Graphic Method of Developing the Lengths and Bevels of 
the Various Rafters Used in Framing an Equal-Pitch Roof 


B to S is the developed length of jack rafters No. 5, 
No. 6 and No. 7. 

Angle J is the level cut for all common and jack 
rafters. 

Angle N is the level cut for the hip and valley rafters. 

Angle K is the plumb cut for all common and jack 
rafters. 

Angle M is the plumb cut for the hip and valley 
rafters. 



























57 


HOW TO FRAME A ROOF OF EQUAL PITCH 

Angle 1 is the top cut for the jack rafters. 

Runs and Lengths of Raftevs .—The following table 
is prepared to assist the student in checking up his 
work. It is intended that the framer will take his runs 
from the layout and develop the lengths with the steel 
square and fence, using the tables only as a matter of 
information, giving him assurance that he has taken 
the propei runs and determined the proper lengths of 
the rafters. The measurements listed in the table are 
the extreme lengths on the center lines. Make allow¬ 
ances for the cutting length where rafters intersect a 
ridge, hip or valley rafter. It is suggested that the 
reader frame a model of the roof for practice, building 
it to the same scale as the layout, 1" to the foot. In 
using the table to check the model read feet as inches; 

for example, the nm of hip A .-.aid read 10and 

the length 12-^-. The square being laid out in 

twelfths of an inch, it is an easy matter to check the 
work up accurately. 


RUNS AND LENGTHS OF RAFTERS USED IN FRAMING ROOF 

OF EQUAL PITCH 


Number of 
Rafters 

Quantity of 

Rafters 

Runs 

Lengths 

Kind of Rafters 

1 

1 pair 

2'0" 

2'6" 

Jack Rafters 

2 

1 pair 

4'0" 

5'0" 

Jack Rafters 

3 

1 pair 

6'0" 

7'6" 

Jack Rafters 

4 

20 

T 6" 

9'414" 

Common Rafters 

5 

1 pair 

6'6" 

8'iy>" 

Jack Rafters 

6 

1 pair 

4'6" 

5'7y>" 

Jack Rafters 

7 

1 pair 

2'6" 

3'iy," 

Jack Rafters 

A 

1 

10'714" 

12'0i/s" 

Hip Rafters 

B 

1 

10'7i4" 

12'0i/ 8 " 

Valley Rafters 

C 

2 

12'6" 

12'6" 

Ridge 
















58 


COURSE IN ROOF FRAMING 


Figures to use on the steel square: 

Common, and jack rafters 9" on the tongue and 12" 
on the blade. Mark on tongue for plumb cuts and on 
blade for level cuts. 

Top cut for jack rafters, 12" on tongue and 15" on 
blade. Mark on the blade for top cut. 

Hip and valley rafter, 9" on tongue and 17" on 
blade. Mark on tongue for j3lumb cuts and on blade for 
level cuts. 

Top cut for hip and valley rafters, 8%" on tongue 
and 9%" on blade. Mark on the blade for top cut. 


CHAPTER IV 


SEVEN PROBLEMS FOR PRACTICE IN 

EQUAL PITCH 


FRAMING ROOFS OF 


In the preceding- chapters the terms used in roof- 
raming have been outlined and sections of roofs have 
been analyzed to demonstrate the application of the 
underlying fundamental principles involved. To make 
this instruction effective it must be coupled with prac¬ 
tice. V ith this object in view and with the further idea 
of developing seli confidence and increased performance 
in the use of the steel square and particularly in fram- 
ing a loot, these problems are offered. They will serve 
as excellent exercises for individual practice and train¬ 
ing and will greatly reduce the time usually spent in 
the industry acquiring similar information. 

These plans are representative of the better class of 
roofs for residences; containing a variety of hips, val- 
jack, ciipple and common rafters. In making 
layouts tor these roofs some attention and thought 
should be given to designing. This is an important fea¬ 
ture as many styles of roofs may be developed over the 
same plates. The architectural design should be con- 
y e u t ^ o f a residential section is de¬ 

pendent on the grace and pleasing appearance of its 
buildings. The buildings themselves may be laid out 
and equipped with all the conveniences at the command 
of an architect or owner and an ugly roof would over¬ 
balance all of these. The outer appearance of a build- 

59 


60 


COURSE IN ROOF FRAMING 


ing is the first thing that greets the eye of a prospective 
buyer and if he is not satisfied with the exterior it is 
doubtful if he will take the time and trouble to look 
at the interior. 

The strength of die roof should be considered. It 
should be so framed as to carry its own weight without 
sagging and, especially in sections where heavy snow 
falls occur, it should be strong enough to resist the re¬ 
sulting weight. 

Where possible all hips and valleys should have some 
tie with the ridge and plate and, although the entire 
length of a hip or valley rafter may not be used to give 
the desired outer effects of the roof, it will make a 
much stronger roof to run these timbers through, tying 
the walls together and making a more even distribu¬ 
tion of the weights and strains likely to come upon the 
roof. Whether or not an attic is to be finished should 
be considered in designing a roof. More head room 
will be needed if the attic is to be finished than if it 
is to be left rough. 

The general instructions given for laying out the 
previous problems should be followed in framing the 
following roofs. Make a working layout of each plan, 
full size, representing 1" to the foot. It is suggested 
that the reader make models of the various roofs to the 
same scale as the layout. The figures on the plans are 
given in inches. To apply them full size read them 
as feet. Take the runs of the rafters from the lavout. 
Develop the lengths with the steel square and fence. 
Number each rafter and ridge on the layout and for 
ready identification put the corresponding numbers on 


SEVEN PROBLEMS FOR PRACTICE 


61 


the rafters as they are laid out. Lay off the position 
of each rafter on the plate and ridge, properly spaced. 
Lay out a profile of a common rafter on the layout for 
each different pitch roof so that the height of the plate 
level can be determined. Having done so, measure the 
distance from planclier level to the plate level and note 
the measurements in the specifications. 

For the convenience of the framer a suitable distance 
is noted in the specifications preceding each problem. 
These measurements should be checked up and the 
method of determining the two levels should be thor¬ 
oughly understood before proceeding. The specifica¬ 
tions suggest suitable sizes of stock that can be used 
for practice framing without losing the practical appli¬ 
cation of any of the principles involved. The tables 
following each problem are intended only as a matter 
of information to give assurance to the framer that he 
has used the proper runs and determined the correct 
length of the rafters and they should be referred to 
only as a check upon his own work. The measurements 
listed are extreme lengths on the center lines. Make 
allowances where rafters intersect a ridge, hip or 
valley rafter. 

In checking up a model built to a scale of 1" to the 
foot, read the figures in the tables as inches. For 

example, on rafter No. 1 in the table following problem 

71/" 

No. 1, the run would read 2" and the length 2—g- 

The square being laid out in twelfths of an inch, it is 
an easy matter to check up the work accurately. 

The projection, pitch, and width of facias in the 



62 


COURSE IN ROOF FRAMING 


various problems differ to give variety and to stimulate 
interest. These figures can be further changed if de¬ 
sired, but the lengths in the accompanying tables will 
apply only to roofs for the particular pitch listed in the 
specifications preceding each problem. Should the pitch 
be changed, these lengths will change accordingly. 


PROBLEM NO. 1 


Specifications .—Plate %" x 2". 

Hip and valley rafters, %" x 1 
Common and jack rafters, %" x 
Ridge, %" x 1V S ". 

Projection, 2". 

Facia, 

Plancher level to plate level, 1%". 
Pitch, 10" rise in one foot (5/12 
pitch). 

Dimensions, see plan, Figure 20. 
Rafters spaced 2" on centers. 


In framing a roof special attention should be given 
to the method of framing the rafters into each other. 
They should be framed so as to give solid nailing and 
strong bracing. Referring to the plan, Figure 20, the 
ridges, hips and valleys form the skeleton or backbone 
of the roof and carry most of the load. The jack, 
cripple and common rafters help to distribute the 
weight, but without a strong and rigid tie of the main 
rafters the roof would be weak and likely to collapse. 
Valleys B form a butt joint. Where two hips intersect 
a ridge, as hips A and ridge G, Figure 20, the ridge 


SEVEN PROBLEMS FOR PRACTICE 


63 




















































































64 


COURSE IN ROOF FRAMING 


should run between them. See enlarged section, Fig¬ 
ure 21. 

To Determine the Length of Ridge G .—Lay in hips A, 
valleys B and ridge G, full size as shown in Figure 21. 
The run of ridge G taken from the layout, Figure 20, is 
5" on the center lines as shown by C-E , Figure 21. 
From this length deduct one-lialf the thickness of valley 


i 



Figure 21.—Section Through Ridge G, Showing a Method of Deter¬ 
mining the Length of the Ridge 

B, measured on he line of the ridge, or one-half the 
diagonal thickness of valley B, as at C-D, Figure 21. 
To this length add on the other end of the ridge the 
same amount as deducted, E-F, Figure 21, and also add 
one-lialf the thickness of ridge G, as at F-G, Figure 21. 
This brings the outside end of the ridge in line with 
the short points of the bevel joint of hips A against 
ridge G. 

If the reason for making these deductions and addi- 





















SEVEN PROBLEMS FOR PRACTICE 


65 


tions is clear, it will readily be seen that the length of 
the ridge is equal to the run pins one-half the thickness 
ol the ridge F-G, or 5 3/16", the measurements being 
taken on the center line. To make a fit against the 
side ot valley B draw a miter, or angle of forty-five 
degrees, through the length on the center line on the 
top edge of the ridge. 



Figure 22.—Section Through Ridge H, Showing a Method for Deter¬ 
mining the Length of the Ridge and for Fitting into the 
Intersection of Valleys B and D 

To Determine the Length of Ridge LI .—The run of 
ridge II, taken from the layout, Figure 20, is 14" on 
the center lines as shown at C-E, Figure 22. From 
this length deduct one-half the thickness of valley B 
measured on the line of ridge II, or one-half the diag¬ 
onal thickness of valley B as at C-D, Figure 22. To 
make a fit into the intersection of valleys B and D draw 
a miter or angle of forty-five degrees, right and left 
hand, through the length on the center line on the top 
edge of the ridge as shown in Figure 22. 

To Lay Out Ilips A .—Set the fence and square at 
10" rise on the tongue and 17" run on the blade. Mark 
on the tongue for all plumb cuts and on the blade for 





















66 


COURSE IN ROOF FRAMING 


all level cuts. The run of hip A is taken from the 
layout, Figure 20, measuring from the return corner of 

83 /" 

the facia line to the center of ridge G, or 12—— • 


Press the fence firmly against the top edge of the stock 
to be used and produce the facia or first plumb line 
to the extreme left, A, Figure 23. Slide the fence to 
the right and measure on a level line from facia line A 


the run of the hip, and produce line C, Figure 

23, the extreme length of the hip rafter on the center 
line. From this length deduct one-lialf the thickness 
of the ridge measured on the line of hip A, or one-half 
the diagonal thickness of ridge G as at E-H, Figure 
21, y 4 ", and produce plumb line D. Square this line 
across the top edge of the rafter and locate the center 
point. 

To lay out the top cut so that the hip rafter will fit 
against the side of the ridge measure forward on a 
level line from plumb line D a distance equal to one- 
half the thickness of the stock used for the hip, 
and produce plumb line 1. Connect plumb line 1 
through plumb line D on the top edge and produce bevel 
2 as shown in the top view, Figure 23. This top cut 
can also be laid out with the steel square by using 9%" 
(the bridge measure of one-half of the run 17" and 
one-lialf the rise 10") on the blade and 8y 2 " (one-half 
the run 17") on the tongue. Mark on the blade for 
the top cut. 

To complete the lower end of the rafter measure in 
on a level line from facia line A the diagonal distance 




SEVEN PROBLEMS FOR PRACTICE 


67' 


of tlie projection 2" x 2", or 2 10/12", and produce wall 
line B. Measure down on facia line A from the top 
edge of the rafter the width of the facia, and pro¬ 
duce planclier level F. Measure up from planclier level 
F, 1%", locating plate level G. 

To make the return on the facia line at the corner of 
the building square facia line A across the top edge of 



the rafter and locate the center point, measure in on 
a level line from facia line A, on either side of the 
rafter, a distance equal to one-half the thickness oi the 
stock used for the hip, and produce plumb line 3. 
Connect plumb line 3 with the center point on the facia 
line as shown at 4, top view, Figure 23. This top cut is 
the same as the top cut at the upper end of the rafter, 
the same figures on the square giving the cut. 

To determine the amount of backing so that the center 




















68 


COURSE IN ROOF FRAMING 


line of the hip will come in alignment with the top edges 
of the common and jack rafters, first gauge a line 
through the center of the rafter on the top edge. Then 
produce a level line anywhere on the side of the rafter. 
On this level line measure off a distance equal to one- 
half the thickness of the stock used, from the top 
edge as at M, Figure 23. Through this point gauge a 
line parallel to the top edge. Remove the corner of the 
stock between this line and the center line for the 
amount of backing. 


Cut on line A, on bevels 4 for the facia, on line F 
for the plancher level, on lines G and B for the birds- 
moutli and on plumb line 1, on bevel 2 for the joint 
against the side of the ridge. 

To Lay Out Hip E .—Use the same figures on the 
square as those used in laying out hip A. Take the 
run from the layout, Figure 20, measuring from the 
intersection of the center lines of ridge G and valleys B 
and the intersection of the center lines of ridge F and 

AW' 


hip C, or 2 


12 


Press the fence firmly against the top 


edge of the stock to be used for the hip and produce 
the first plumb line A to the extreme left, Figure 24. 
Slide the fence to the right and measure on a level line 


from plumb line A the run of the hip, 2 


1 y 2 


rr 


12 


and pro¬ 


duce plumb line C, the extreme length of the hip on 
the center lines. From the bottom end deduct one-lialf 
the thickness of valley B, or and produce plumb 

line D, which is a square butt joint against valley B, 
valley B and hip E intersecting at right angles. From 




SEVEN PROBLEMS FOR PRACTICE 


69 


the top end deduct one-half the thickness of the ridge 
measured on the line of the hip rafter, or one-half the 
diagonal thickness of ridge F, and produce plumb 
line 3. Square this line across the top edge of the 



rafter and locate the center point. 

To lay out the top cut so that the hip will fit against 
the ridge at the proper angle measure back on a level 
line from plumb line 3 a distance equal to one-half the 
thickness of the stock used for the hip, and pro- 












70 


COURSE IN ROOF FRAMING 


duce plumb line 1. Connect plumb line 1 through plumb 
line 3 on the top edge and produce bevel 2 as shown 
in the top view, Figure 24. This top cut can also be 
laid out with the steel square by using the same figures 
as those given for laying out the top cut for hips A. 



Figure 25.—Front and Right Side Elevation, Problem 1, Showing Method 

of Framing the Rafters 

Back the hip rafter on either side according to the 
rules for backing described for backing hips A. Cut 
on line I) for the butt joint against the side of valley B 
and on plumb line 4, on bevel 2 for the cut against 
the side of ridge F. 

This gives an outline of the method of developing the 






SEVEN PROBLEMS FOR PRACTICE 


71 


length of the rafters and ridges which should enable the 
reader to complete the roof. 

To Assemble the Roof .—Assemble the rafters as 
shown in the elevations, Figures 25 and 26. Set up 
valleys B first. Then valley D and ridge H, locating 



Figure 26.—Rear and Left Side Elevation, Problem 1, Showing Method 

of Framing the Rafters 

the proper height of ridge B with a pair of common 
rafters No. 22. Then set up hips A, ridge G and lastly 
hip C and ridge F, locating the proper height of ridge 
F with a pair of common rafters No. 6. Particular 
attention should be paid in fastening the rafters to keep 









72 


COURSE IN ROOF FRAMING 


the center lines and top edges in alignment. Notice that 
the top edges of the ridges are not in alignment with 
the center lines of the hip and valley rafters but dropped 
to overcome the need for backing the ridges, the roof 
hoard continuing the lines of the roof to the extreme 
height. 


RUNS AND LENGTHS OF RAFTERS USED IN FRAMING 
PROBLEM NO. 1—5/12 PITCH 


Number of 
Rafters 

Quantity of 
Rafters 

Runs 

Lengths 

Kind of Rafters 

1 

3 pair 

2' 0" 

2' 71,4" 

Jack Rafters 

2 

2 1/2 pair 

4' 0" 

5' 2i/," 

Jack Rafters 

3 

1 2/2 pair 

6' 0" 

7' 9%" 

Jack Rafters 

4 

1 2/2 pair 

8' 0" 

10' 5" 

Jack Rafters 

5 

1 

10' 0" 

13' 614" 

Jack Rafter 

6 

10 

10' 6" 

13' 8" 

Common Rafters 

7 

1 

10' 6" 

13' 8" 

Jack Rafter 

8 

1 

8' 6" 

11' 0%" 

Jack Rafter 

9 

1 

6' 6" 

8' 514" 

Jack Rafter 

10 

1 

4' 6" 

5'10!4" 

Jack Rafter 

11 

1 

2' 0" 

2' 714" 

Cripple Rafter 

12 

1 

2' 0" 

2' 714" 

Jack Rafter 

13 

1 

4' 0" 

5' 21/," 

Jack Rafter 

14 

2 

5' 0" 

6' 6i/s" 

Cripple Rafters 

15 

1 

8' 0" 

10' 5" 

Jack Rafter 

16 

1 

6' 0" 

7' 9%" 

Jack Rafter 

17 

1 

4' 0" 

5' 214" 

Jack Rafter? 

18 

4 

3' 0" 

3'10%" 

Cripple Rafters 

19 

1 pair 

2' 0" 

2' 714" 

Jack Rafters 

20 

1 pair 

4' 0" 

5' 2i/," 

Jack Rafters 

21 

1 pair 

6' 0" 

7' 9%" 

Jack Rafters 

22 

8 

7' 0" 

9' 1%" 

Common Rafters 

A 

1 pair 

12' 8%" 

14' 914" 

Hip Rafters 

B 

1 pair 

12' 8%" 

14' 914" 

Valley Rafters 

C 

1 

14'10i/ 8 " 

17' 2%" 

Hip Rafter 

D 

1 

9'10%" 

11' 57 8 " 

Valley Rafter 

E 

1 

2' li/" 

2' 514" 

Hip Rafter 

F 

1 

13' 6" 

13' 6" 

Ridge 

G 

1 

5' 0" 

5' 0" 

Ridge 

H 

1 

14' 0" 

14' 0" 

Ridge 















SEVEN PROBLEMS FOR PRACTICE 


73 


Figures used on the steel square: 

Common, jack and cripple rafters, 10" on tongue, 
12" on blade. Mark on tongue for plumb cuts and on 
blade for level cuts. 

Top cut for jack and cripple rafters, 12" on tongue, 
15%" on blade. Mark on blade for top cut. 

Hip and valley rafters, 10" on tongue, 17" on blade. 
Mark on tongue for plumb cuts and on blade for level 
cuts. 

Top cut for hips and valleys, 8*4 " on tongue, 9%" 
on blade. Mark on blade for top cut. 


PROBLEM NO. 2 


Specifications. 


Plate, %"x 214". 

Hip and valley rafters, %" x 1%". 
Common and jack rafters, %" x y 8 ". 
Ridge, %" x 1V 8 ". 


Projection, 2". 


. Facia, %". 

Plancher level to plate level, 2". 

Pitch, 12" rise in one foot (y 2 pitch). 

Dimensions (see plan, Figure 27). 

Rafters spaced 2" on centers. 

In framing the main rafters run hips B and C from 
ridge N to the plate, giving support for valleys I) and 
II. Run valley F from the facia line to ridge K, giving 
support for valley E. 

Hip B should be backed the entire length on one side 
and from ridge N to the intersection of valley II on the 
other side. Hip C should be backed the entire length on 



74 


COURSE IN ROOF FRAMING 



Figure 27.—Plan of Problem No. 2, from Which the Working- Layout 

Is Made 































































































SEVEN PROBLEMS FOR PRACTICE 


75 


one side and from ridge N to the intersection of valley D 
oil the other side. 

1 o Assemble the Roof .—Assemble the rafters as 



Figure 28.—Front and Right Side Elevation, Problem 2, Showing the 

Method of Framing the Rafters 


shown in the elevations, Fignres 28 and 29. Set up 
ridge N first, supported by hips, A, B and C. Next set 
up valley H and ridge L, supported by a pair of No. 13 
common rafters. Then valley D and ridge M supported 
by a pair of No. 13 common rafters. Then liip I, valley 








76 


COURSE IN ROOF FRAMING 


G and ridge K, supported by a pair of No. 23 common 
rafters. Lastly valleys E and F and ridge J, supported 
by a pair of No. 29 common rafters. 



Figure 29.—Rear and Left Side Elevation, Problem 2, Showing the 

Method of Framing the Rafters 


RUNS AND LENGTHS OF RAFTERS USED IN FRAMING 

PROBLEM NO. 2—% PITCH 


Number of 
Rafters 

Quantity of 
Rafters 

Runs 

Lengths 

Kind of Rafters 

1 

1 pair 

2' 0" 

2'10" 

Jack Rafters 

2 

1 

4' 0" 

5' 77s" 

Jack Rafter 

3 

1 

6' 0" 

8' 57s" 

Jack Rafter 

4 

1 

8' 0" 

11' 3%" 

Jack Rafter 

5 

1 pair 

9' 0" 

12' 8%" 

Jack Rafters 

6 

1 pair 

7' 0" 

910% " 

Jack Rafters 

7 

1 pair 

5' 0" 

7' 07 s " 

Jack Rafters 

8 

2 

2' 0" 

210" 

Cripple Rafters 
























SEVEN PROBLEMS FOR PRACTICE 


77 


RUNS AND LENGTHS OF RAFTERS USED IN FRAMING 
PROBLEM NO. 2—y> PITCH—Continued 


Number of 

Rafters 

Quantity of 
Rafters 

Runs 

Lengths 

Kind of Rafters 

9 

2 pair 

1' 0" 

1' 5" 

Jack Rafters 

10 

2 pair 

3' 0" 

4' 2%" 

Jack Rafters 

11 

1 pair 

5' 0" 

7' 0%" 

Jack Rafters 

12 

1 pair 

7' 0" 

9'10%" 

Jack Rafters 

13 

10 

7' 0" 

9'10%" 

Common Rafters 

14 

1 pair 

4' 0" 

5' 7%" 

Jack Rafters 

15 

1 pair 

6' 0" 

8' 5%" 

Jack Rafters 

16 

1 pair 

8' 0" 

11' 3%" 

Jack Rafters 

17 

1 pair 

1' 0" 

1' 5" 

Jack Rafters 

18 

1 pair 

3' 0" 

4' 2%" 

Jack Rafters 

19 

1 

5' 0" 

7' 0 7 / s " 

Jack Rafter 

20 

1 

V 0" 

1' 5" 

Jack Rafter 

21 

1 

r 0" 

9'10%" 

4' 2%" 

Jack Rafter 

22 

1 

3' 0" 

Jack Rafter 

23 

4 

7' 0" 

9'10%" 

7' 0%" 

Common Rafters 

24 

1 

5' 0" 

Jack Rafter 

25 

1 

T 0" 

9'10%" 

Jack Rafter 

26 

1 pair 

2' 0" 

2'10" 

Jack Rafters 

27 

1 pair 

4' 0" 

5' 7%" 

Jack Rafters 

28 

1 pair 

6' 0" 

8' 5%" 

Jack Rafters 

29 

16 

6' 0" 

8' 5%" 

Common Rafters 

30 

1 

4' 0" 

5' 7%" 

Cripple Rafter 

31 

1 

8' 0" 

11' 3%" 

Cripple Rafter 

32 

1 

2' 0" 

2'10" 

Cripple Rafter 

33 

3 

4 > 0 " 

5' 7%" 

Cripple Rafters 

A 

1 

12' 8%" 

15' 7" 

Hip Rafter 

B 

1 

9'10%" 

12' li/o" 

Part Hip and 

Part Valley 

C 

1 

9'10%" 

12 ' iy 2 " 

Part Hip and 

Part Valley 

D 

1 

9'10%" 

12' iy," 

Valley Rafter 

E 

1 

8' 5%" 

10' 4%" 

Valley Rafter 

F 

1 

9'10%" 

12' iy," 

Valley Rafter 

G 

1 

9'10%" 

12' 11/“" 

Valley Rafter 

H 

1 

9'10 %" 

12' li/o" 

Valley Rafter 

I 

1 

7' 0%" 

8' 7%" 

Hip Rafter 

J 

1 

22' 0" 

22' 0" 

Ridge 

K 

1 

13' 0" 

13' 0" 

Ridge 

L 

1 

11' 0" 

11' 0" 

Ridge 

M 

1 

9' 0" 

9' 0" 

Ridge 

N 

1 

6' 0" 

6' 0" 

Ridge 




























78 


COURSE IN ROOF FRAMING 


Figures used on the steel square: 

Common, jack and cripple rafters, 12" on tongue, 12" 
on blade. Mark on tongue for plumb cuts and on blade 
for level cuts. 

Top cut for jack and cripple rafters, 12" on tongue, 
17" on blade. Mark on blade for top cut. 

Hip and valley rafters, 12" on tongue, 17" on blade. 
Mark on tongue for plumb cuts and on blade for level 
cuts. 

Top cut for liip and valley rafters, 8%" on tongue, 
10%" on blade. Mark on blade for top cut. 

PROBLEM NO. 3 

Specifications. —Plate, %" x 2". 

Hip and valley rafters, %" x 114 ". 

Common and jack rafters, %" x %". 

Ridge, %"xl%". 

Projection, 114". 

Facia, y 2 ". 

Planclier level to plate level, 1%". 

Pitch, 9" rise in one foot (% pitch). 

Dimensions (see plan, Figure 30). 

Rafters spaced 2" on centers. 

In framing the main rafters run hips B and D from 
ridge H to the plate, giving support for valleys E 
and F. 

Hip B should be backed the entire length on one side 
and from ridge H to the intersection of valley E on 


SEVEN PROBLEMS FOR PRACTICE 


79 


the other side. Hip D should be backed the entire length 
on one side and from ridge H to the intersection of 
valley F on the other side. 

To Assemble the Roof .—Assemble the rafters as 



Figure 30.—Plan of Problem 3, from Which the Working Layout Is Made 


shown in the elevations, Figures 31 and 32. Set. up 
ridge E first, supported by hips A , B, C and D. Then 
valley E and ridge /, supported by a pair of No. 18 
common rafters. Lastly valley F and ridge G , sup¬ 
ported by a pair of No. 25 common rafters. 















































































































80 


COURSE IN ROOF FRAMING 



Figure 31.—Front and Right Side Elevation, Problem 3, Showing the 

Method of Framing the Rafters 



Figure 32.—Rear and Left Side Elevation, Problem 3, Showing the 

Method of Framing the Rafters 







SEVEN PROBLEMS FOR PRACTICE 


81 


RUNS AND LENGTHS OF RAFTERS USED IN FRAMING 

PROBLEM NO- 3—% PITCH 


Number of 
Rafters 

Quantity of 
Rafters 

Runs 

Lengths 

Kind of Rafters 

1 

2 pair 

2'0" 

2'6" 

Jack Rafters 

2 

3 pair 

4'0" 

5'0" 

Jack Rafters 

3 

3 pair 

6'0" 

7'6" 

Jack Rafters 

4 

3 pair 

8'0" 

lO'O" 

Jack Rafters 

5 

3 pair 

lO'O" 

12'6" 

Jack Rafters 

6 

3 pair 

12'0" 

15'0" 

Jack Rafters 

7 

1 pair 

14'0" 

17'6" 

Jack Rafters 

8 

iy* pair 

14'0" 

17'6" 

Jack Rafters 

9 

1 

14'0" 

17'6" 

Common Rafter 

10 

1 

13'0" 

16'3" 

Jack Rafter 

11 

1 

ll'O" 

13'9" 

Cripple Rafter 

12 

1 

7'0" 

8'9" 

Cripple Rafter 

13 

1 

3'0" 

3'9" 

Cripple Rafter 

14 

1 pair 

2'6" 

3'iy," 

Jack Rafters 

15 

1 pair 

4'6" 

5'7'/>" 

Jack Rafters 

16 

1 

6'6" 

8'li/V' 

Jack Rafter: 

17 

1 

8'6" 

10'7i/“" 

Jack Rafter 

18 

12 

8'6" 

10'7i/i" 

Common Rafters 

19 

1 

ll'O" 

13'9" 

Cripple Rafter 

20 

1 

7'0" 

8'9" 

Cripple Rafter 

21 

1 

3'0" 

3'9" 

Cripple Rafter 

22 

1 pair 

2'6" 

3'1V>" 

Jack Rafters 

23 

1 

4'6" 

5'7i/k' 

Jack Rafter 

24 

1 

6'6" 

8'iy>" 

Jack Rafter 

25 

10 

6'6" 

8'iy>" 

Common Rafters 

A 

1 

19'9%" 

22'4%" 

Hip Rafter 

Part Hip and 

B 

1 

17'8 1 / s " 

20'0i/s" 

Part Valley 

C 

1 

19'9%" 

22'4%" 

Hip Rafter 

Part Hip and 

D 

1 

17'81/s" 

20'0i/s" 

Part Valley 

E 

1 

12'0i4" 

13'7i/i" 

Valley Rafter 

F 

1 

9'21/p' 

10'4%" 

Valley Rafter 

G 

1 

16'6" 

16'6" 

Ridge 

H 

1 

4'0" 

4'0" 

Ridge 

I 

1 

18'6" 

18'6" 

Ridge 


Figures used on the steel square: 

Common, jack and cripple rafters, 9" on tongue, 12" 
on blade. Mark on tongue for plumb cuts and on blade 
for level cuts. 





















82 


COURSE IN ROOF FRAMING 


Top cut for jack and cripple rafters, 12" on tongue, 


15" on blade. Mark on blade for top cut. 

Hip and valley rafters, 9" on tongue, 17" on blade. 



Mark on tongue for plumb cuts; on blade for level cuts. 
Top cut for hip and valley rafters, 8%" on tongue, 
9%" on blade. Mark on blade for top cut. 






























































































SEVEN PROBLEMS FOR PRACTICE 


S3 


PROBLEM NO. 4 

Specifications. —Plate, %" x 2". 

Hip and valley rafters, %" x 1%". 
Common and jack rafters, %" X 
Ridge, %" x iy 8 ". 

Projection, 1%". 

Facia, %". 

Planclier level to plate level, 1%". 
Pitch, 11" rise in one foot (11/24 
pitch). 

Dimensions (see plan, Figure 33). 
Rafters spaced 2" on centers. 



Figure 34.—Front and Right Side Elevation, Problem 4, Showing the 

Method of Framing the Rafters 



84 


COURSE IN ROOF FRAMING 


In framing the main rafters run hips A, B and D from 
ridge N to the plate and hip E from ridge N to the 
facia line, giving support for valleys C, F, H and /. 
Bun valley H from the facia line to hip B, giving sup¬ 
port for valley G. 



Figure 35.—Rear and Left Side Elevation, Problem 4, Showing the 

Method of Framing the Rafters 

Hip rafter B should he backed the entire length on 
one side and the backing stopped at the intersection of 
ridge K on the other side, beginning at ridge N. Hip 
rafter A should be backed the entire length on one side 
and on the other side the backing should begin at ridge N 
and stop at the intersection of valley I. Hip rafter D 
should be backed the entire length on one side and on 




SEVEN PROBLEMS FOR PRACTICE <^5 

the other side the backing should begin at ridge N 
and stop at the intersection of valley F. 

To Assemble the Roof .—Assemble the- rafters as 
shown m the elevations, Figures 34 and 35. Set up 
ridge N first, supported by hips A, B, D and E. Then 
valley C and ridge K, supported by a pair of No 22 
common rafters. Then valleys H and G and ridge L 
supported by a pair of No. 42 common rafters. Then 
valley / and ridge J, supported by a pair of No. 14 
common rafters. Lastly valley F* and ridge M, sup¬ 
ported by a pair of No. 36 common rafters. 


RUNS AND LENGTHS OF RAFTERS USED 
PROBLEM NO. 4—11/24 PITCH 


IN FRAMING 


Number of 
Rafters 

Quantity of 

Rafters 

Runs 

1 

1 pair 

2' 0" 

2 

1 pair 

4' 0" 

3 

1 pair 

6' 0" 

4 

1 

8' 0" 

5 

1 

10' 0" 

6 

1 

12' 0" 

7 

2 

14' 0" 

8 

1 

12' 0" 

9 

1 

8' 0" 

1G 

1 

4' 0" 

11 

1 pair 

2' 0" 

12 

1 

4' 0" 

13 

1 

6' 0" 

14 

4 

6' 0" 

15 

6 

4' 0" 

16 

1 pair 

2' 0" 

17 

1 pair 

4' 0" 

18 

1 pair 

6' 0" 

19 

1 pair 

8' 0" 

20 

1 

10' 0" 

21 

1 

12' 0" 

22 

10 

12' 0" 

23 

3 

4' 0" 

24 

1 

4' 0" 

25 

1 

8' 0" 


Lengths 


Kind of Rafters 


2' 8y>" 

5' 5 %" 
8' 1%" 
IG'1014" 
13' 6%" 
16' 3%" 
i8'iiy s " 
16' 3%" 
IG'1014 " 
5' 5%" 
2' 8V>" 
5' 5i/s" 
8 ' 1 %" 
8' 1%" 
5' 5i/s" 
2' 8i/>" 
5' 5i/|" 
8 ' 1 %" 
lG'lGi/4" 
13' 6%" 
16' 35/s" 
16' 35/ 8 " 
5' 5i/s" 
5' 5i/s" 
1G'1G14 " 


Jack Rafters 
Jack Rafters 
Jack Rafters 
Jack Rafter 
Jack Rafter. 
Jack Rafter* 
Jack Rafters 
Jack Rafter 
Cripple Rafter 
Cripple Rafter 
Jack Rafters 
Jack Rafters 
Jack Rafter 
Common Rafters 
Cripple Rafters 
Jack Rafters 
Jack Rafters 
Jack Rafters 
Jack Rafters 
Jack Raftert 
Jack Rafter 
Common Rafters 
Cripple Rafters 
Cripple Rafter 
Cripple Rafter 

































86 


COURSE IN ROOF FRAMING 


HUNS AND LENGTHS OF RAFTERS USED IN FRAMING 
PROBLEM NO. 4—11/24 PITCH—Continued 


Number of 
Rafters 

Quantity of 
Rafters 

Runs 

Lengths 

Kind of Rafters 

26 

1 

12' 0" 

16' 35/s" 

Cripple Rafter 

27 

1 

14' 0" 

18'llVs" 

Jack Rafter 

28 

1 

12' 0" 

16' 35/s" 

Jack Rafter 

29 

1 

10' 0" 

13' 6%" 

Jack Rafter 

80 

1 

8' 0" 

lOTOW 

Jack Rafter 

31 

1 

6' 0" 

8' 15/ s " 

Jack Rafter 

32 

1 

4' 0" 

5' 5Vs" 

Jack Rafter 

33 

1 pair 

2' 0" 

2' 8V>" 

Jack Rafters 

34 

1 pair 

4' 0" 

5' 5Vs" 

Jack Rafters 

35 

1 pair 

6' 0" 

8' 15/s" 

Jack Rafters 

36 

4 

10' 0" 

13' 6%" 

Common Rafters 

37 

1 

10' 0" 

13' 6%" 

Jack Rafter 

38 

1 

8' 0" 

10'IOVL" 

Jack Rafter 

39 

1 pair 

2' 0" 

2' 8V2" 

Jack Rafters 

40 

1 pair 

4' 0" 

5' 5Vs" 

Jack Rafters 

41 

1 pair 

6' 0" 

8' 15/s"- 

Jack Rafters 

42 

2 

6' 0" 

8' 15/s" 

Common Rafters 

43 

1 

4' 0" 

5' 5Vs" 

Jack Rafter 

44 

1 

8' 0" 

10'1014" 

Jack Rafter 

45 

3 

8' 0" 

10'1014" 

Cripple Rafters 

A 

1 

17' 4i/ s " 

20'10V>" 

Part Hip and Part 
Valley 

B 

1 

17' 4y 8 " 

2OTOV2" 

Part Hip and Part 
Valley 

C 

1 

16'115/ 8 " 

20' 2%" 

Hip Rafter 

D 

1 

17' 4V 8 " 

20'10V>" 

Part Hip and Part 
Valley 

E 

1 

19' 9%" 

23' 7Vs" 

Hip Rafter 

F 

1 

14' 1 %" 

16'10Vt" 

Valley Rafter 

G 

1 

8' 5%" 

10' 1%" 

Valley Rafter 

H 

1 

11' 3%" 

13' 5%" 

Part Hip and Part 
Valley 

I 

1 

8' 5Vs" 

10' 1%" 

Valley Rafter 

J 

1 

8' 0" 

8' 0" 

Ridge 

K 

1 

20' 0" 

20' 0" 

Ridge 

L 

1 

8' 0" 

8' 0" 

Ridge 

M 

1 

12' 0" 

12' 0" 

Ridge 

N 

1 

2' 0" 

2' 0" 

Ridge 
















87 


SE^ EN PROBLEMS FOR PRACTICE 

Figures used on the steel square: 

Common, jack and cripple rafters, 11" on tongue, 12" 

on blade. Mark on tongue for plumb cuts and on blade 
for level cuts. 

Top cut for jack and cripple rafters, 12" on tonoue 
EM" on blade. Mark on blade for top cut 

Hip and valley rafters, 11" on tongue, 17" on blade. 

Mark on tongue for plumb cuts and on blade for level 
cuts. 

Top cut for hip and valley rafters, 814 " on tongue 
and IO 14 " on blade. Mark on blade for top cut. 


PROBLEM NO. 5 

Specifications. —Plate, %" x 2". 

Hip and valley rafters, %" x 1%". 

Common and jack rafters, %" x %" 

Ridge, %" x 1V 8 ". ' 

Projection, 2". 

Facia, %". 

Plancher level to plate level, l 3 /,". 

Pitch 10" rise in one foot (5/12 
pitch). 

Dimensions (see plan, Figure 36). 

Rafters spaced 2" on centers. 

_ In framing the main rafters run hip B from the facia 
line to ridge I, giving support for valley B. Run hips C 
from ridge K to the wall line, giving support for valleys 
E and G. Run ridge K from the intersection of hips C 
to hip A, giving support for valley D and hip F. 


88 


COURSE IN ROOF FRAMING 


Hip B should be backed the entire length on one side 
and from ridge 7 to the intersection of valley 77 on the 
other side. One hip rafter marked C should be backed 
the entire length on one side and from ridge K to the 



Figure 36.—Plan of Problem 5, from Which the Working Layout Is Macle 


intersection of valley E on the other side. The other 
hip marked C should be backed the entire length on 
one side and from ridge K to the intersection of valley 
G on the other side. 




























































































SEVEN PROBLEMS FOR PRACTICE 


89 


To Assemble the Roof .—Assemble the rafters as 
shown in the elevations, Figures 37 and 38. Set up 
ridge 7 first, supported by hips A and B. Then ridge 
K, supported by hips C. Then valley D and hip F. 



Figure 37.—Front and Right Side Elevation, Problem 5, Showing the 

Method of Framing the Rafters 


Then valley E and ridge J, supported by a pair of 
No. 18 common rafters. Then valley G and ridge L, 
supported by a pair of No. 33 common rafters. Lastly 
valley H and ridge M, supported by a pair of No. 37 
common rafters. 





90 


COURSE IN ROOF FRAMING 



Figure 3 8.—Rear and Left Side Elevation, Problem 5, Showing the 

Method of Framing the Rafters 


RUNS AND LENGTHS OF RAFTERS USED IN FRAMING 
PROBLEM NO. 5—5/12 PITCH 


Number of 
Rafters 

Quantity of 
Rafters 

Runs 

Lengths 

Kind of Rafters 

1 

2 1/2 pair 

2' 0" 

2' 7*4" 

Jack Rafters 

2 

2 1/2 pair 

4' 0" 

5' 2V>" 

Jack Rafters 

3 

1 2/2 pair 

6' 0" 

7' 9%" 

Jack Rafters 

4 

1 2/2 pair 

8' 0" 

10' 5" 

Jack Rafters 

5 

1 2/2 pair 

10' 0" 

13' 014" 

Jack Rafters 

6 

1 2/2 pair 

12' 0" 

15' 71 / 2 " 

Jack Rafters 

7 

2 

14' 0" 

18' 2%" 

Jack Rafters 

8 

1 

14' 0" 

18' 2%" 

Cripple Rafter 

9 

1 

10' 0" 

13' 014" 

Cripple Rafter 

10 

1 

6' 0" 

7' 9%" 

Cripple Rafter 

11 

1 

2' 0" 

2' 714" 

Cripple Rafter 

12 

5 

6' 0" 

7' 9%" 

Cripple Rafters 

13 

1 

4' 0" 

5' 214" 

Cripple Rafter 

14 

5 

2' 0" 

2' 714" 

Cripple Rafters 

15 

1 pair 

2' 0" 

2' 714" 

Jack Rafters 

16 

1 

4' 0" 

5' 2i/," 

Jack Rafter 

17 

1 

6' 0" 

7' 9%" 

Jack Rafter 

18 

5 

6' 0" 

7' 9-%" 

Common Rafters 


















SEVEN PROBLEMS FOR PRACTICE 


91 


RUNS AND LENGTHS OF RAFTERS USED IN FRAMING 
PROBLEM NO. 5—5/12 PITCH—Continued 


Number of 
Rafters 

Quantity of 
Rafters 

Runs 

Lengths 

Kind of Rafters 

19 

1 

6' 0" 

7' 9%" 

Jack Rafter 

20 

1 

4' 0" 

5' 2i/ 2 " 

Cripple Rafter 

21 

1 

8' 0" 

10' 5" 

Cripple Rafter 

22 

1 

12' 0" 

15' 7i/>" 

Jack Rafter 

23 

1 

10' 0" 

13' oy 4 " 

Jack Rafter 

24 

1 

8' 0" 

10' 5" 

Jack Rafter 

25 

1 

6' 0" 

7' 9 

Jack Rafter 

26 

1 

4' 0" 

5' 2V>" 

Jack Rafter 

27 

1 

4' 0" 

5' 21/2" 

Cripple Rafter 

28 

1 

8' 0" 

10' 5" 

Cripple Rafter 

29 

1 pair 

2' 0" 

2' 7%" 

Jack Rafters 

30 

1 pair 

4' 0" 

5' 2i/o" 

Jack Rafters 

31 

1 

6' 0" 

7' 9%" 

Jack Rafter 

32 

1 

8' 0" 

10' 5" 

Jack Rafter 

33 

5 

8' 0" 

10' 5" 

Common Rafters 

34 

1 pair 

1' 0" 

1 ' 35/s" 

Jack Rafters 

35 

1 pair 

3' 0" 

3'10%" 

Jack Rafters 

36 

1 pair 

5' 0" 

6 ' 6y s " 

Jack Rafters 

37 

1 pair 

7' 0" 

9' 13/ s " 

Jack Rafters 

38 

1 

12' 0" 

15' 714" 

Jack Rafter 

39 

1 

10' 0" 

13' O 1 ^" 

Jack Rafter 

40 

1 

2' 0" 

2' 7%" 

Jack Rafter 

A 

1 pair 

19'95/ s " 

22'll 3 / 4" 

Hip Rafters 

B 

1 

19'9%" 

22'11%" 

Part Hip and part 
Valley 

C 

1 pair 

14'1%" 

16' 5" 

Part Hip and Part 
Valley 

D 

1 

16'115/ s " 

19' 83/g" 

Valley Rafter 

E 

1 

8'5%" 

9' 1014" 

Valley Rafter 

F 

1 

2 ' 10" 

3' 33/ s " 

Hip Rafter 

G 

1 

11'3%" 

13' 1%" 

Valley Rafter 

H 

1 

9'10%" 

11' 5%" 

Valley Rafter 

I 

1 

2 ' 0" 

2' 0" 

Ridge 

J 

1 

10' 0" 

10' 0" 

Ridge 

K 

1 

6' 0" 

6' 0" 

Ridge 

I, 

1 

10' 0" 

10' 0" 

Ridge 

M 

1 

7' 0" 

7' 0" 

Ridge 


Figures used on the steel square: 

Common, .jack and cripple rafters, 10" on tongue, 12" 
on blade. Mark on tongue for all plumb cuts and on 
blade for all level cuts. 



















92 


COURSE IN ROOF FRAMING 


Top cut for jack and cripple rafters, 12" on tongue, 
15%" on blade. Mark on blade for top cut. 

Hip and valley rafters, 10" on tongue, 17" on blade. 
Mark on tongue for all plumb cuts and on blade for all 
level cuts. 

Top cut for hip and valley rafters, 8%" on tongue, 
9%" on blade. Mark on blade for top cut. 


PROBLEM NO. 6 

Specifications .—Plate, %" x 2 y 2 ". 

Hip and valley rafters, %" x 1^4". 

Common and jack rafters, %" x %". 

Ridge, %" x iy 8 ". 

Projection: main roof, 2"; dormer, 1". 

Facia: main roof, %"; dormer, %". 

Plancher level to plate level: main 
roof, 2"; dormer, 1". 

Pitch, 12" rise in one foot (y 2 pitch). 

Dimensions (see plan, Figure 39). 

Rafters spaced 2" on centers. 

In framing the main rafters run hip B from ridge L 
to the facia line, giving support for valleys C and E. 
Run valley E from hip B to the facia line, giving sup¬ 
port for valley D. Run valley F from ridge L to the 
wall line, giving support for valley G and ridge 0. Run 
ridge Q from the wall line to valley F, giving support 
to valley J, hip K and valley H. Run valley H from 
the wall line by ridge Q , giving support for the dormer 
formed by valley 1 and ridge P. 

Hip B should be backed the entire length on one 


SEVEN PROBLEMS FOR PRACTICE 


93 


side and fiom ridge L to the intersection of valley C 
on the other side. Hip F should be backed the entire 
length on one side and from ridge L to the intersection 
of valley G on the other side. 



Figure 39.—Plan of Problem 6, from Which the Working Layout Is Made 


A section through the dormer is shown in Figure 40. 
This shows a method for determining the height of the 
dormer plate above the main plate of the building. The 
dormer is formed by the intersection of valleys 77 and 7. 


































































































































94 


COURSE IN ROOF FRAMING 



Figure 40.—Section Through Dormer, Problem 6, Showing a Method of 
Determining the Height of the Dormer Plate Above the Main 

Plate of the Building 



































SEVEN PROBLEMS FOR PRACTICE 


95 



The outside walls of the dormer are built up on the 
top of jack laltcis No. 52 and No. 53, which makes the 
run of dormer common rafters No. 62, 3 3/16" plus the 
projection, 1", or a total run of 4 3/16". Draw a profile 
of dormer common rafter No. 62 as shown in Figure 40 


Figuie 41. Front and Right Side Elevation, Problem ti, Showing the 

Method of Framing the Rafters 

and determine the plate level and birdsmoutli in ac¬ 
cordance with the requirements of the specifications. 
Draw the center line of ridge P and from the intersec¬ 
tion of valleys II, I and ridge P mark off the run of the 
ridge, 8", and produce the wall line. Through the point 
of intersection of the two wall lines as at S, Figure 40, 
draw in the top edge of common rafter No. 53 and 







96 


COURSE IN ROOF FRAMING 


develop the plate level and birdsmouth of the main 
rafters in accordance with the requirements of the 
specifications. Measure out from wall line B, 2", the 
width of the projection, and produce facia line A. 
Measure down on facia line A from the top edge of the 
rafter %", and produce plancher level F. Measure up 



Figure 42.—Rear and Left Side Elevation, Problem 6, Showing the 

Method of Framing the Rafters 

from plancher F, measuring on a plumb line, 2", locat¬ 
ing plate level G. The distance from the main plate level 
to the top of the dormer plate, or 5", gives the height of 
the dormer plate above the main plate of the building. 
If the studding is placed on the top edge of common 
rafter No. 53 the height of the plate above the top edge 
of the rafter will be 4%". 






SEVEN PROBLEMS FOR PRACTICE 


97 


To Assemble the Hoof .—Assemble the rafters as 
shown in the elevations, Figures 41 and 42. Set up 
ridge L first, supported by hips A, B and F. Then 
valley G and ridge 0, supported by a pair of No. 35 
common rafters. Then ridge 0, supported by a pair of 
No. 58 common rafters. Then valley J and hip K. 
Then valleys II and I. Build up the dormer plate and 
then ridge P, supported by a pair of dormer common 
rafters No. 62. Then set up valleys E and D and ridge 
N, supported by a pair of common rafters No. 23. 
Lastly set up valley C and ridge M, supported by a pair 
of common rafters No. 14. 


RUNS AND LENGTHS OF RAFTERS USED IN FRAMING 

PROBLEM NO. 6—% PITCH 


Number of 
Rafters 

| Quantity of 
Rafters 

Runs 

Lengths 

Kind of Rafters 

1 

2 pair 

2' 0" 

2'10" 

Jack Rafters 

2 

iy 2 pair 

4' 0" 

5' 7 Vs" 

Jack Rafters 

3 

1 pair 

6' 0" 

8' 5%" 

Jack Rafters 

4 

1 pair 

8' 0" 

11' 3%" 

Jack Rafters 

5 

1 pair 

10' 0" 

14' 1%" 

Cripple Rafters 

6 

1 

10' 0" 

14' 1 %" 

Cripple Rafter 

7 

1 

10' 0" 

14' 1%" 

Cripple Rafter 

8 

1 

8' 0" 

11' 3%" 

Cripple Rafter 

9 

1 

4' 0" 

5' 7%" 

Cripple Rafter 

10 

1 pair 

2' 0" 

2'10" 

Jack Rafters 

11 

1 pair 

4' 0" 

5' 7Vs" 

Jack Rafters 

12 

1 pair 

6' 0" 

8' 5Vs" 

Jack Rafters 

13 

1 pair 

8' 0" 

11' 3%" 

Jack Rafters 

14 

1 pair 

10' 0" 

14' 1%" 

Jack Rafters 

15 

10 

2' 0" 

2'10" 

Jack Rafters 

16 

1 

6' 0" 

8' 5Vs" 

Cripple Rafter 

17 

1 

4' 0" 

5' 7Vs" 

Cripple Rafter 

18 

1 pair 

2' 0" 

2'10" 

Jack Rafters 

19 

1 pair 

4' 0" 

5' 7Vs" 

Jack Rafters 

20 

1 pair 

6' 0" 

8' 5Vs" 

Jack Rafters 

21 

1 pair 

8' 0" 

11' 3 % " 

Jack Rafters 

22 

1 pair 

10' 0" 

14' 1%" 

Jack Rafters 























98 


COURSE IN ROOF FRAMING 


RUNS AND LENGTHS OF RAFTERS USED IN FRAMING 
PROBLEM NO. 6—14 PITCH—Continued 


Number of 
Rafters 

Quantity of 
Rafters 

Runs 

Lengths 

Kind of Rafters 

23 

8 

10' 0" 

14' 1%" 

Common Rafters 

24 

1 

2' 0" 

2'10" 

Cripple Rajfter 

25 

1 

5' 0" 

7' 0%" 

Jack Rafter 

26 

1 

7' 0" 

9'10%" 

Jack Rafter 

27 

1 

9' 0" 

12' 8%" 

Jack Rafter 

28 

1 

11' 0" 

15' 6%" 

Jack Rafter 

29 

1 

12' 0" 

16'11%" 

Jack Rafter 

30 

1 

12' 0" 

16'11%" 

Jack Rafter 

31 

1 

10' 0" 

14' 1%" 

Jack Rafter 

32 

1 

8' 0" 

11' 3%" 

Jack Rafter 

33 

1 

6' 0" 

8' 5%" 

Jack Rafter 

34 

1 

4' 0" 

5' 7%" 

Jack Rafter 

35 

3 

9' 0" 

12' 8%" 

Common Rafters 

36 

1 pair 

5' 0" 

7' 0%" 

Jack Rafters 

37 

1 pair 

3' 0" 

4' 2%" 

Jack Rafters 

38 

1 pair 

1' 0" 

1' 5" 

Jack Rafters 

39 

1 

7' 0" 

9'10%" 

Jack Rafter 

40 

1 

9' 0" 

12' 8%" 

Jack Rafter 

41 

1 

2' 0" 

2'10" 

Cripple Rafter 

42 

1 

6' 0" 

8' 5%" 

Cripple Rafter 

43 

1 

9' 0" 

12' 8%" 

Jack Rafter 

44 

1 pair 

1' 0" 

1' 5" 

Cripple Rafters 

45 

1 

11' 0" 

15' 6%" 

Jack Rafter 

46 

1 

13' 0" 

18' 4%" 

Jack Rafter 

47 

1 

8' 0" 

11' 3%" 

Jack Rafter 

48 

1 

6' 0" 

8' 5%" 

Jack Rafter 

49 

1 

4' 0" 

5' 7%" 

Jack Rafter 

50 

1 

2' 0" 

2'10" 

Jack Rafter 

51 

1 

5' 0" 

7' 0?4" 

Jack Rafter 

52 

1 

7' 0" 

9'10%" 

Jack Rafter 

53 

1 

7' 0" 

9'10%" 

Jack Rafter 

54 

I 

5' 0" 

7' 0%" 

Jack Rafter 

55 

1 

2' 0" 

2'10" 

Cripple Rafter 

56 

1 

6' 0" 

8' 5%" 

Jack Rafter 

57 

1 

8' 0" 

11' 3%" 

Jack Rafter 

58 

2 pair 

13' 0" 

18' 4%" 

Common Rafters 

59 

1 pair 

2' 0" 

2'10" 

Jack Rafters 
Dormer 

60 

1 pair 

4' 0" 

5' 7%" 

Jack Rafters 
Dormer 

61 

2 

4' 2 U" 

5'11" 

Common Rafters 
Dormer 

62 

2 

4' 214" 

5'11" 

Common Rafters 
Dormer 



























SEVEN PROBLEMS FOR PRACTICE 


99 


RUNS AND LENGTHS OF RAFTERS USED IN FRAMING 
PROBLEM NO. 6—PITCH—Continued 


Number of 
Rafters 

Quantity of 
Rafters 

Runs 

Lengths 

Kind of Rafters 

63 

1 

1' 0" 

1' 5" 

Jack Rafter 

64 

1 

3' 0" 

4' 2%" 

Jack Rafter 

65 

1 

5' 0" 

7' 0%" 

Jack Rafter 

66 

1 

7' 0" 

9'10%" 

Jack Rafter 

67 

1 

9' 0" 

12' 8%" 

Jack Rafter 

68 

1 

11' 0" 

15' 65/ s " 

Jack Rafter 

60 

1 

13' 0" 

18' 45/ s " 

Jack Rafter 

70 

1 

2' 0" 

2'10" 

Cripple Rafter 

71 

1 

5' 0" 

7' 0%" 

Jack Rafter 

72 

1 

7' 0" 

9'10%" 

Jack Rafter 

73 

1 

9' 0" 

12' £%" 

Jack Rafter 

74 

1 

11' 0" 

15' 65/s" 

Jack Rafter 

75 

1 

12' 0" 

16'115/ 8 " 

Jack Rafter 

76 

1 

12' 0" 

16'11%" 

Jack Rafter 

A 

1 

21' 2y," 

25'11%" 

Hip Rafter 

B 

1 

. 

21' 2*4" 

25'11%" 

Part Hip and 

Part Valley 

C 

1 

14' 1%" 

17' 3%" 

Valley Rafter 

D 

1 

14' 1%" 

17' 3%" 

Valley Rafter 

E 

I 

18' 45/s" 

22' 6%" 

Valley Rafter 

F 

1 

18' 45/ s " 

22' 6*4" 

Part Hip and 

Part Valiev 

G 

1 

12' 8%" 

15' 7" 

Valley Rafter 

H 

1 

14' 1%" 

17' 3%" 

Valley Rafter 

I 

1 

9'10%" 

12' iy>" 

Valley Rafter 

J 

1 

18' 45/ s " 

22' 614" 

Valley Rafter 

K 

1 

2' 10" 

3' 55/ s " 

Hip Rafter 

L 

1 

8' 0" 

8' 0" 

Ridge 

M 

1 

10' 0" 

10' 0" 

Ridge 

N 

1 

18' 0" 

18' 0" 

Ridge 

0 

1 

11' 0" 

11' 0" 

Ridge 

P 

1 

8' 0" 

8' 0" 

Ridge Dormer 

Q 

1 

19' 0" 

19' 0" 

Ridge 


Figures used on the steel square: Common, jack and 
cripple rafters, 12" on tongue, 12" on blade. Mark on 
tongue for plumb cuts and on blade for level cuts. 

Top cut for jack and cripple rafters, 12" on tongue, 
17" on blade. Mark on blade for top cut. 

Hip and valley rafters, 12" on tongue, 17" on blade. 


> * 
> o ) 


* ^ 























100 


COURSE IN ROOF FRAMING 




Mark on tongue for plumb cuts and on blade for level 
cuts. 

Top cut for liip and valley rafters, 8%" on tongue, 
10%" on blade. Mark on blade for top cut. 


PROBLEM NO. 7 

Specifications. —Plate, main roof, %" x 2". 

Plate A around to B, %" x 5". 

Hip and valley rafters, %" x 

Common and jack rafters, %" x 
Ridge, %" x 1V 8 ". 

Projection, 2V>". 

Facia, y 2 ". 

Plancher level to plate level, 1%". 

Pitch, 9" rise in one foot (% pitch). 

Dimensions (see plan, Figure 43). 

Rafters spaced 2" on centers. 

In framing the main rafters run hip A from ridge N, 
forming a butt joint against valley C, to the plate, 
giving support for valley B and ridge L. Run valley 
K from valley II to the wall line, giving support for 
valley J, hip I and ridge Q. 

Hips A and G and valleys B, C, H and K all cross 
the plate at an angle of forty-five degrees and are laid 
out in the usual way for hip and valley rafters of equal 
pitch roofs. 

Valleys D and J and hips E, F and I are laid out 
differently because they do not cross the plate at an 
angle of forty-five degrees and the same figures on the 
square will not apply. In each case it is necessary to 


SE\ EN PROBLEMS FOR PRACTICE 


101 



Figure 43. Plan of Problem 7, from Which the Working Layout Is Made 























































































































102 


COURSE IN ROOF FRAMING 


determine the rise in inches per foot run before the 
length can be determined. 

To Lay Out Valley D .—First determine the exact 
location of the valley on the plan by drawing light con¬ 
struction lines at right angles from the intersection of 
the two facia lines A, Figure 44, as at J and K. With 
A as a center and anv convenient radius, arc the con- 
struction lines as at L and M. With L and M as centers 
and a convenient radius, bisect the angle as at N. 
From A, at the intersection of the two facia lines, draw 
in the center line of valley D through arc N until it 
intersects ridge P. Measure the run on the plan, A to R, 
Figure 44, or 11". Before setting the fence and square, 
the rise in inches per foot of run must be determined. 
The height of ridge P will give the total height of 
valley D. 


The run of common rafter No. 33 is 10 y 2 feet. 

The rise, 9" in one foot. 

Therefore, the total height of valley D will be 9xl0y 2 , 
or 94 y 2 ". 


Rise in inches 
Run in feet 


= rise in inches per foot, or 8 7/12". 


That is, the rise in inches divided by the run in feet 
will give the rise in inches per foot run. 

Working this out as given in the problem we have: 


94V 2 -f-ll = M X — 

2 11 


8 - 


7 


ff 


12 


= rise in inches per 


foot. 


Set the fence and square at 8 7/12" rise on the tongue 
and 12" run on the blade. Mark on the tongue for all 




SEVEN PROBLEMS FOR PRACTICE 


103 
























104 


COURSE IN ROOF FRAMING 


plumb cuts aucl on the blade for all level cuts. Press 
the fence firmly against the top edge of the stock to 
be used and produce the facia or first plumb line to the 
extreme right, A y Figure 45. Slide the fence to the left 
and measure on a level line from facia line A the run 
of the valley, 11", and produce plumb line R, the ex¬ 



treme length of valley D to the center of ridge P. From 
this length deduct one-half the thickness of the ridge 
measured on the line of vallev D or one-lialf the diagonal 
thickness of ridge 0 as at R-U, Figure 44, and produce 
plumb line U, Figure 45. Square this line across the 
top edge of the rafter and locate the center. 

To lay out the top cut so that the valley mil fit 




















SEVEN PROBLEMS FOR PRACTICE 


105 


into the intersection of ridges P and 0, lay in a section 
of the valley full size as shown in Figure 44. At the 
point where the outside edge of the rafter intersects 
ridge P square a line across at right angles to the 
center line until it intersects the center line as at V, 
h igure 44. Measure forward on a level line from 
plumb line U, Figure 45, the distance U-V, Figure 44, 
and produce plumb line V, Figure 45. Connect plumb 
line T with the center line on the top edge as at 2, top 
view, Figure 45. Side B is a square cut on plumb line 
U as at 3. 

To complete the lower end of the rafter measure in 
on a level line from facia line A the diagonal distance 
of the projection A-B, Figure 44, 2%", and produce 
wall line B. 

To eliminate notching into the crotch formed by the 
intersection of the two walls move wall line B out the 
distance B-T, Figure 44, and produce plumb line T, 
Figure 45. Measure down on facia line A, the 

width of the facia, and produce plancher level F. 
Measure up from plancher level F, 1%", locating plate 
level G. 

To make the return on the facia line square facia 
line A across the top edge of the rafter and locate the 
center point. Measure forward on a level line from 
facia line A y on either side of the rafter, the distance 
A-S, Figure 44, and produce plumb line S, Figure 45. 
Connect plumb line S with the center point on the facia 
line as shown at 1 , top view, Figure 45. Cut on plumb 
line S and top cut 1 for the facia, on lines T and G 


106 


COURSE IN ROOF FRAMING 


for the birdsmouth, on plumb line V, top cut 2, plumb 
line U and top cut 3 for the fit against the ridge. 

To Lay Out Hip E— It will be necessary to de¬ 
termine how hips E, F and G and ridge P are to be 



Figure 46.—Section Through Hips E, F. and G and Ridge P, Figure 43, 
Showing a Method of Framing the Rafters Together 

framed into each other. One method is shown in 
Figure 46. Next, to determine the rise in inches per 
foot of run measure the run on the plan, A-X, Figure 
48, or 1111/12". The height of ridge P will give the 
total height of hip E. 










SEY T EN PROBLEMS FOR PRACTICE 


107 


Run of common rafter No. 33 is 10y 2 ". 

Rise, 9" in one foot. 

Therefore, the total height of ridge P will be 9x1014, 
or 9414". 


Rise in inches 
Run in feet 


= Rise in inches 


per foot , or 7 11/12". 



Figure 47.—Developed Length of Hip E 

Working this out as given in the problem, we have: 
94 i/o -h 1111/12 = 189/2 143/12 = 489/2 x 13/143 = 

7 11/12 — rise in inches. 


Set the fence and square at 711/12" rise on the 
tongue and 12" run on the blade. Mark on the tongue 

































10S 


COURSE IN ROOF FRAMING 


for all plumb cuts and on the blade for all level cuts. 
Press the fence firmly against the top edge of the stock 
to be used and produce the facia or first plumb line to 
the extreme left, A, Figure 47. Slide the fence to the 
right and measure on a level line from facia line A 
the run of hip E, 1111/12", and produce plumb line M, 
the extreme length to the center line of ridge P. From 
this length deduct the distance M-E, Figure 46, and pro¬ 
duce plumb line N, Figure 47. Square this line across 
the top edge of the rafter and locate the center point. 

To lay out the top cut so that the hip will fit against 
the side of hip F, lay in a section of the hip, full size, 
as shown in Figure 46. At the point where the outside 
edge of liip E intersects the outside edge of hip F square 
a line across at right angles to the center line until it 
intersects the center line as at 0, Figure 46. Measure 
forward on a level line from plumb line N , Figure 47, the 
distance N-O, Figure 46, and produce plumb line 0, 
Figure 47. Connect plumb line 0 through the center 
line on the top edge as at 5, top view, Figure 47. 

To complete the lower end of the rafter measure in on 
a level line from facia line A the diagonal distance of 
the projection, A-B, Figure 48, 210/12" and produce 
wall line B, Figure 47. 

To make a fit against the side of the plate at the 
proper angle, lay in a section of the hip as shown in 
Figure 48. At the point where the outside edge of the 
hip intersects the wall line, square a line across at 
right angles to the center line until it intersects the 
center line as at T , Figure 48. Measure forward on 
the side of the hip from Avail line B the distance T-B, 


SEVEN PROBLEMS FOR PRACTICE 


109 


Figme 48, and produce plumb line T, Fignre 47. Square 
plumb line B across the bottom edge of the rafter and 
connect plumb line T through this center point as shown 
at 6, bottom view. Measure down on facia line A y 2 '\ 
the width of the facia, and produce plancher level F. 



Measure up from plancher level F 1%", locating* plate 
level G. 

To make the turn on the facia line lay in a section 
of the hip full size as shown in Fignre 48. Where the 
outside edges of the hip intersect either facia line draw 
lines across at right angles to the center line until 

































110 


COURSE IN ROOF FRAMING 


they intersect the center line as at R and S. On side A 
of the rafter measure back the distance A-S, Figure 48, 
and produce plumb line S, Figure 47. On side B 
measure back the distance A-R, Figure 48, and produce 
plumb line R , Figure 4/. Connect these two plumb 
lines with the center point on the facia line on the top 
edge of the hip as shown at 4 and 5, top view, Figure 47. 
Cut on plumb line 7?, bevel 5, plumb line S and bevel 4 
for the facia, on lines T and G and bevel 6 for the birds- 
mouth and on plumb line 0 and top cut 3 for the tit 
against the side of hip F. 

To Bach Hip E .—Produce a level line on either side 
of the hip. On side A from the top edge, on this level 
line, point off the distance AS, Figure 48, as shown 
at 1, Figure 47. On side B from the top edge, on this 
level line, point off the distance A-R, Figure 48, as 
shown at 2, Figure 47. Gfauge a line through points 
1 and 2 on either side of the rafter and also through 
the center on the top edge. Remove the corner between 
these lines as shown in the end view, Figure 47. 

To Lay Out Hip F .—Hip F tits against the side of 
ridge P as shown in Figure 46. Measure the run on 
the plan from facia line A to X , Figure 48, or 12 8 / 12 ". 
Next determine the rise in inches per foot of run. 
The total height of the rafter is the same as hip E 
or 94V>". 


Rise in inches D • . . 7 , , „ r 0 // 

—- 7 — ? ——=Rise in inches per foot, or 7 5/12 . 

Run in feet 

Working this out as given in the problem, we have: 
94 1/2 -5-12 8/12 = 189/2 -f-152/12 = 189/2 x 12/152 = 
7 5/12 " — rise in inches per foot. 



SEVEN PROBLEMS FOR PRACTICE 


111 


Set the fence and square at 7 5/12" rise on the tongne 
and 12" run on the blade. Mark on the tongue for all 
plumb cuts and on the blade for all level cuts. Press 
the fence firmly against the top edge of the stock to be 
used and produce the facia or first plumb line to the 
extreme left, A, Figure 49. Slide the fence to the right 



and measure on a level line from facia line A the run of 
hip F, 12 8/12", and produce plumb line M, the extreme 
length to the center line of ridge P. From this length 
deduct the distance M-N, Figure 46, and produce plumb 
line N, Figure 49. Square this line across the top edge 
of the rafter and locate the center point. 



























112 


COURSE IN ROOF FRAMING 


To lay out tlie top cut so that the hip will fit against 
the side of ridge P, lay in a section of the hip, full size, 
as shown in Figure 46. At the point where the outside 
edge of the hip intersects the outside edge of ridge P 
square a line across at right angles to the center line 
until it intersects the center line as at 0, Figure 46. 
Measure forward on a level line from plumb line N, 
Figure 49, the distance N-O, Figure 46, and produce 
plumb line 0, Figure 49. Connect plumb line 0 through 
the center line on the top edge as at 3, top view, 
Figure 49. 

To complete the lower end of the rafter measure in 
on a level line from facia line A the diagonal distance 

of the projection, A-B, Figure 48, 3-^2" and produce 

1 2 

wall line B, Figure 49. 

To make a fit against the side of the plate at the 
proper angle, lay in a section of the hip as shown in 
Figure 48. At the point where the outside edge of the 
hip intersects the wall line square a line across at right 
angles to the center line until it intersects the center 
line as at T, Figure 48. Measure forward on the side of 
the hip from wall line B, the distance T-B, Figure 48, 
and produce plumb line T, Figure 49. Square wall line B 
across the bottom edge of the rafter, locate the center 
point, and connect plumb line T through this center 
point as. shown at 6, bottom view, Figure 49. Measure 
down on facia line A from the top edge of the rafter 
i/o", the width of the facia and locate planclier level F. 
Measure up from planclier level F, 1%", locating plate 
level G . 



SEVEN PROBLEMS FOR PRACTICE 


113 


To make the return on the facia line lay in a section 
of the hip, full size, as shown in Figure 48. Where the 
outside edges of the hip intersect the facia line, draw 
lines across at right angles to the center line until they 
intersect the center line as at R and 8. On side A of 
the rafter measure hack the distance A-R, Figure 48, 
and produce plumb line R, Figure 49. On side B 
measure back the distance A-8, Figure 48, and produce 
plumb line 8, Figure 49. Connect these two plumb lines 
with the center point on the facia line on the top edge 
as shown at 4 and 5, top view, Figure 49. Cut on plumb 
line R, bevel 4, plumb line 8 and bevel 5 for the facia; 
on lines T and G and bevel 6 for the birdsmouth and on 
plumb line 0 and top cut 3 for the tit against ridge P. 

To Bach Hip F .—Produce a level line on either side 
of the rafter. On side A, from the top edge, on this level 
line, point off the distance A-R, Figure 48, as shown at 

1, Figure 49. On side B, from the top edge, on this level 
line, point off the distance A-S, Figure 48, as shown at 

2, Figure 49. Gauge a line through the points 1 and 2 
on either side of the rafter and also through the center 
on the top edge. Remove the corner between these lines 
as shown in the end view, Figure 49. 

To Lay Out Hip 1 .—Measure the run on the plan 
from the intersection of hip K and valley J and the 
intersection of ridges N and 0 as shown in the section 
M to R, Figure 50, or 10'1". 

Next determine the rise in inches per foot of run. 
The extreme height of the hip is determined by the run 
of common rafter No. 70. 



114 


COURSE IN ROOF FRAMING 





























SEVEN PROBLEMS FOR PRACTICE 


115 


Run of common rafter No. 70— 20'0" 

Rise 9" in one foot — 

Therefore, the total height of hip 1 will be 9x20, or 180". 


The height of the lower end of the hip is determined 
by the extreme height of valley J. Project a line on the 
plan parallel with ridge Q from the intersection of hip 
K, valley J and hip / as shown in Figure 50. Measure 
the run from this line to the facia line as H to J, or 
10'6". Multiplying this run by 9" rise in one foot will 
give the height of the lower end of hip 1, or 94% 


Extreme height of hip I — 180" 

Lower height of hip I — 94%" 

Height hip l rises in its non= 85%" 


Rise in inches 
Run in feet 


= rise in inches per foot, or 


tm 


Working this out as given in the problem we have: 
85 1/2 -r-10 1/12 = 171/2 -T-121/12 = 171/2 x 12/121 = 


5 % 

12 


rise in inches per foot. 


Set the fence and square at 8^4" on the tongue and 

12" on the blade. Mark on the tongue for all plumb 
cuts and on the blade for all level cuts. Press the 
fence firmly against the top edge ot the stock to be used 
and produce the first plumb line M, Figure 51, to the 
extreme right. Slide the fence to the left and measure 
on a level line from plumb line M the run of hip 1, or 
10 1/12", and produce plumb line R, the extreme length 
to the intersection of ridges N and 0. From this length 








116 


COURSE IN ROOF FRAMING 


deduct the distance R-W, Figure 50, and produce plumb 
line W, Figure 51. Square this line across the top 
edge and locate the center point. 

To lay out the top cut so that the hip will fit against 
the sides of ridges N and 0 lay in a section of the hip, 



full size, as shown in Figure 50. At the point where the 
outside edge of hip / intersects ridge 0 , square a line 
across at right angles until it intersects the center line 
as at V. Likewise square a line across at right angles 
to the center line from the point W until it intersects 
the outside edge of the rafter as at X. On side B 



















SEVEN PROBLEMS FOR PRACTICE 


117 


measu forward on a level line from plumb line W, 
Figure 51, the distance W-V, Figure 50, and produce 
plumb line V, Figure 51. On side A measure back on a 
level line from plumb line W the distance X-Y, Figure 
50, and produce plumb line Y, Figure 51. Connect 
plumb line Y with the center point on the top edge as 
at 4. Connect plumb line V with the center point on 
the top edge as at 5, top view, Figure 51. 

To complete the lower end of the rafter, first de¬ 
termine the top cut by drawing in a section of the 
hip, full size, as shown in Figure 50. Where the out¬ 
side edge of the hip intersects hip K, square a line 
across at right angles to the center line until it inter¬ 
sects the center line as at 0. Measure back on a level 
line from plumb line M, Figure 51, the distance M-N, 
Figure 50, and produce plumb line A 7 , Figure 51. Square 
this line across the top edge of the rafter and locate 
the center point. Measure in from plumb line N the 
distance N-O, Figure 50, and produce plumb line O, 
Figure 51. Connect plumb line O through the center 
point on the top edge as shown at 3, Figure 51. Cut on 
plumb line O and bevel 3 for the fit against the side of 
hip K, on plumb line V and top cut 5 for the fit against 
the side of ridge O and on plumb line Y and top cut 4 
for the fit against the side of ridges O and N. 

To Bach Hip I. —Produce a level line on either side 
of the rafter. On side A, from the top edge, on this 
level line, point off the distance X-Y, Figure 50, as 
shown at 2, Figure 51. On side B, from the top edge, 
on this level line, point off the distance V-W, Figure 



118 


COURSE IN ROOF FRAMING 


50, as shown at 1, Figure 51. Gauge a line through the 
points 1 and 2 on either side of the hip and also through 
the center on the top edge. Remove the corner between 
these lines as shown in the end view, Figure 51. 

To Lay Out Valley J .—Measure the run on the plan 
from the facia line to the intersection of hips I and K, 
A-M, Figure 50, or ll'lO". Next determine the rise in 
inches per foot. The total height of valley J was de¬ 
termined in laying out the preceding hip / which was 
found to be 94%". 


Rise in inches 


rise in incites per foot, or 8". 


Run in feet 

Working this out as given in the problem, we have: 


94 1/2 -r- 1110/12 = 189/2 h- 142/12 = 189/2 x 12/142 = 
8" rise in inches per foot. 


Set the fence and square at 8" rise on the tongue 
and 12" run on the blade. Mark on the tongue for all 
plumb cuts and on the blade for all level cuts. Press 
the fence firmly against the top edge of the stock to be 
used and produce the first plumb line to the extreme 
right, or facia line A, Figure 52. Slide the fence to the 
left and measure on a level line from facia line A, 
the run of valley J, or 1110/12", and produce plumb 
line M, the extreme length to the center of hip K. From 
this length deduct the distance M-N, Figure 50, and 
produce plumb line N, Figure 52. Square this line 
across the top edge and locate the center point. 

To lay out the top cut so that the valley will fit 



SEVEN PROBLEMS FOR PRACTICE 


119 


against the side of hip K, lay in a section of the valley, 
full size, as shown in Figure 50. At the point where 
the outside edge of the valley intersects the outside 
edge ot hip K square a line across at right angles to 
the center line until it intersects the center line as at 0, 



Figure 50. Measure forward on a level line from 
plumb line N, Figure 52, the distance N-O, Figure 50, 
and produce plumb line 0, Figure 52. Connect plumb 
line 0 through this center point on the top edge as shown 
at 2 , top view, Figure 52. 
























120 


COURSE IN ROOF FRAMING 


To complete the lower end of the valley measure in 
on a level line from facia line A the diagonal distance 

of the projection A-B , or 2?^-", and produce wall line B. 

Measure down on facia line A from the top edge of 
the rafter the width of the facia, and produce 

plancher level F. Measure up from plancher level F 
1%", and locate plate level G. 

To make the return on the facia line and to determine 
the distance to advance the wall line lay in a section of 
the valley, full size, as shown in Figure 50. Where the 
outside edge of the valley intersects the plate square a 
line across at right angles to the center line until it 
intersects the center line as at T, Figure 50. Also 
square a line across from facia line A at right angles 
to the center line until it intersects the outside edge of 
the valley. To advance the wall line to avoid notching 
into the crotch of the building measure forward the 
distance B-T, Figure 50, from plumb line B, and pro¬ 
duce plumb line T, Figure 52. 

To make the return on the facia line, square facia line 
A across the top edge and locate the center point. 
From plumb line A measure forward the distance A-S, 
Figure 50, and produce plumb line S, Figure 52. Con¬ 
nect plumb line 8 on either side of the valley with the 
facia line on the center point on the top edge as shown 
at 1, Figure 52. Cut on plumb line 8 and top cut 1 
for the facia, on lines T and G for the birdsmouth 
and on plumb line O and top cut 2 for the tit against 
hip K, 



Figure 53.—Front and Right Side Elevation, Problem 7, Showing the 

Method of Framing the Rafters 


SEVEN PROBLEMS FOR PRACTICE 


121 










122 


COURSE IN ROOF FRAMING 


To Assemble the Iloof .—Assemble the rafters as 
shown in the elevations, Figures 53 and 54. Set up 
hips A and C first. Then ridge M, supported by a pair 
of No. 14 common rafters. Then valley B and ridge L, 
supported by a pair of No. 1 common rafters. Then 
hips F and G and ridge P, supported by a pair of No. 



Figure 54.—Rear and Left Side Elevation, Problem 7, Showing the 

Method of Framing the Rafters 


33 common rafters and the hip E, noticing that hips E 
and F do not intersect the corner of the building be¬ 
cause they do not cross the plate at an angle of forty- 
five degrees. They must intersect on the facia line. 
Then set up valley D, ridges N and 0 and lastly valleys 
H, J and K, hip 1 and ridge Q, supported by a pair of 
No. 59 common rafters. 






2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

OO 

oo 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 


SEVEN PROBLEMS FOR PRACTICE 


123 


ND LENGTHS OF RAFTERS USED IN FRAMING 
PROBLEM NO. 7—% PITCH 


Quantity of 
Rafters 

Runs 

Lengths 

Kind of Ratfers 

10 

12' 6" 

15' 7y>" 

Common Rafters 

1 

12' 6" 

15' 7y 2 " 

Jack Rafter 

1 

10' 6" 

13' iy>" 

Jack Rafter 

1 pair 

8' 6" 

10' 7y> 

Jack Rafters 

1 pair 

6' 6" 

8' iy>" 

Jack Rafters 

1 pair 

4' 6" 

5' 7y> 

Jack Rafters 

1 pair 

2' 6" 

3' iy 2 " 

Jack Rafters 

1 

5' 0" 

6' 3" 

Cripple Rafter 

1 

9' 0" 

11' 3" 

Cripple Rafter 

1 

13' 0" 

16' 3" 

Cripple Rafter 

1 

16' 0" 

20' 0" 

Jack Rafter 

1 

18' 0" 

22' 6" 

Jack Rafter 

1 

20' 0" 

25' 0" 

Jack Rafter 

13 

20' 0" 

25' 0" 

Common Rafters 

1 

15' 0" 

18' 9" 

Jack Rafter 

1 

13' 0" 

16' 3" 

Jack Rafter 

1 

11' 0" 

13' 9" 

Jack Rafter 

1 pair 

9' 0" 

11' 3" 

Jack Rafter 

1 pair 

7' 0" 

8' 9" 

Jack Rafters 

1 pair 

5' 0" 

6' 3" 

Jack Rafters 

1 pair 

3' 0" 

3' 9" 

Jack Rafters 

1 

1' 0" 

1' 3" 

Jack Rafters 

1 

11' 0" 

13' 9" 

Cripple Rafter 

1 

12' 4y>" 

15' 5%" 

Cripple Rafter 

1 

13' 9" 

17' 214" 

Cripple Rafter 

1 

15' 11/ 2 " 

i8'ioy s " 

Cripple Rafter 

1 

13' 9" 

17' 21,4" 

Jack Rafter 

1 

13' iy>" 

16' 4%" 

Jack Rafter 

1 

12' 6" 

15' 7y>" 

Jack Rafter 

1 

li'ioy," 

i4'ioy s " 

Jack Rafter 

1 

8' iy." 

10' iy 8 " 

Cripple Rafter 

1 

5' 8" 

7' 1" 

Jack Rafter 

9 

10' 6" 

13' iy>" 

Jack Rafters 

1 

9' 5" 

ii' 9%" 

Jack Rafter 

1 

5' 9y>" 

7' 2%" 

Jack Rafter 

1 

2' oy 2 " 

2' 6%" 

Jack Rafter 

1 

10' 7" 

13' 2 %" 

Jack Rafter 

1 

5' 4" 

6' 8" 

Jack Rafter 

1 

2' 31/0" 

2'10%" 

Jack Rafter 

1 

5' 3" 

6' 6%" 

Jack Rafter 

1 

8' 3" 

10' 3%" 

Jack Rafter 

1 pair 

10' 0" 

12' 6" 

Jack Rafters 

1 pair 

8' 0" 

10' 0" 

Jack Rafters 

1 pair 

6' 0" 

7' 6" 

Jack Rafters 





























45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 

61 

62 

63 

64 

65 

66 

67 

68 

69 

70 

71 

72 

73 

74 

75 

76 

77 

78 

79 

A 

B 

C 

D 

E 

F 

G 

H 


COURSE IN ROOF FRAMING 


.ND LENGTHS OF RAFTERS USED IN FRAMING 
PROBLEM NO. 7—% PITCH—Continued 


Quantity of 




Rafters 

Runs 

Lengths 

Kind of Rafters 


1 pair 

4' 0" 

5' 0" 

Jack Rafters 

1 pair 

2' 0" 

2' 6" 

Jack Rafters 

1 

10' 7*4" 

13' 3%" 

Jack Rafter 

1 

11' 4" 

14' 2" 

Jack Rafter 

1 

12' oy 2 " 

15' 0%" 

Jack Rafter 

1 

12' 9" 

15'llU" 

Jack Rafter 

1 

13' 8" 

17' 1" 

Jack Rafter 

1 

12' 4y>" 

15' 5%" 

Jack Rafter 

1 

11' 1" 

13'10 1 / 4" 

Jack Rafter 

1 

9' 9y>" 

12' 2%" 

Jack Rafter 

1 

8' 6" 

io' 7y>" 

Jack Rafter 

1 

7' 2y," 

9' oy 8 " 

Jack Rafter 

1 

6' 0" 

7' 6" 

Jack Rafter 

1 

4' 0" 

5' 0" 

Jack Rafter 

4 

13' 0" 

16' 3" 

Common Rafters 

1 pair 

9' 0" 

11' 3" 

Jack Rafters 

1 pair 

7' 0" 

8' 9" 

Jack Rafters 

1 pair 

5' 0" 

6' 3" 

Jack Rafters 

1 pair 

3' 0" 

3' 9" 

Jack Rafters 

1 pair 

1' 0" 

1' 3" 

Jack Rafters 

1 

4' 0" 

5' 0" 

Jack Rafter 

1 

4' iy>" 

5' iy 8 " 

Cripple Rafter 

1 

2' 4" 

2'11" 

Cripple Rafter 

1 

7' 9" 

9' 8 y 4 " 

Cripple Rafter 

1 

17' 0" 

21' 3" 

Jack Rafter 

5 

20' 0" 

25' 0" 

Jack Rafters 

1 

19' 0" 

23' 9" 

Jack Rafter 

1 

17' 0" 

21' 3" 

Jack Rafter 

1 

15' 0" 

18' 9" 

Jack Rafter 

1 

13' 0" 

16' 3" 

Jack Rafter 

1 

12' 0" 

15' 0" 

Jack Rafter 

1 

10' 0" 

12' 6" 

Jack Rafter 

1 

8' 0" 

10' 0" 

Jack Rafter 

1 

6' 0" 

7' 6" 

Jack Rafter 

1 

4' 0" 

5' 0" 

Jack Rafter 

1 

24' 9" 

28' 0 y s " 

Part Hip and 

Part Valley 

1 

17' 8y s " 

28' oy 8 " 

Valley Rafter 

1 

24' oy 2 " 

27' 2y>" 

Valley Rafter 

1 

11' 0" 

13' 3" 

Valley Rafter 

1 

ll'll" 

14' 3y>" 

Hip Rafter 

1 

12' 8" 

14'11" 

Hip Rafter 

1 

i4'ioy s " 

16' 9%" 

Hip Rafter 

1 

16'11%" 

19' 2y>" 

Valley Rafter 

























SEVEN PROBLEMS FOR PRACTICE 


125 


RUNS AND LENGTHS OF RAFTERS USED IN FRAMING 
PROBLEM NO. 7—% PITCH—Continued 


Number of 
Rafters 

Quantity of 
Rafters 

Runs 

Lengths 

Kind of Rafters 

I 

1 

10' 1" 

12' 3i/o" 

Hip Rafter 

J 

1 

1110" 

14' 3" 

Valley Rafter 

K 

1 

1410%" 

16' 9%" 

Part Hip and 

Part Valley 

L 

1 

20' 6" 

20' 6" 

Ridge 

M 

1 

24' 0" 

24' 0" 

Ridge 

N 

1 

11' 0" 

11' 0" 

Ridge 

0 

1 

19' 0" 

19' 6" 

Ridge 

P 

1 

11' 4" 

11' 4" 

Ridge 

Q 

1 

13' 0" 

13' 0" 

Ridge 


Figures used on the steel square: 

Common, jack and cripple rafters, 9" on tongue, 12" 
on blade. Mark on tongue for all plumb cuts and on 
blade for all level cuts. 

Top cut for jack and cripple rafters, intersecting a 
hip or valley rafter that crosses the plate at an angle 
of 45 degrees, 12" on tongue, 15" on blade. Mark on 
blade for top cut. 

Hip and valley rafters that cross the plate at an angle 
of 45 degrees, 9" on tongue, 17" on blade. Mark on 
tongue for all plumb cuts and on blade for all level cuts. 

Top cut for hip and valley rafters that cross the 
plate at an angle of 45 degrees, 8V 2 " on tongue, 9%" 
on blade. Mark on blade for top cut. 

7" 

Valley Z), 8 — 9 on tongue, 12" on blade. 

-1 — 

11 " 

Hip E, on tongue, 12" on blade. 

Hip F, on tongue, 12" on blade. 

























126 


■COURSE IN ROOF FRAMING 


51 / " 

Hip 1, 8 -^ - on tongue 12" on blade. 

Valley J, 8" on tongue, 12" on blade. 

Mark on tongue for all plumb cuts and on blade for 
all level cuts. 

Top cut for valleys D and J and hips E, F and I; 
refer to the text for method of determining these top 
cuts. 



CHAPTER V 


HOW TO FRAME A ROOF OF UNEQUAL PITCH 

An unequal pitch roof is a roof formed by the inter¬ 
section of two roof surfaces having different pitches, 
one surface sloping more than the other. The hip and 
valley rafters form the dividing line, the roof surface 
on one side of the rafters being framed to one pitch and 
the roof surface on the opposite side of the rafters to 
a greater or lesser pitch. 

The plates for the two roof surfaces are at different 
heights, those on the short common side or steeper pitch 
being higher than the plates on the long common side 
or lower pitch. The hip and vadey rafters travel the 
diagonal distance of an oblong with reference to the 
plate in comparing them with the framing of a hip and 
valley rafter for a roof of equal pitch which travels the 
diagonal distance of a square and crosses the plate at 
an angle of forty-five degrees. 

The center lines of the hip and valley rafters must 
intersect the facia line at the extreme corners or re¬ 
turns on the facia line and because they travel the 
diagonal distance of an oblong they are thrown to one 
side of the corner of the building or the return walls, 
crossing the plates to an angle at one side of the corner 
of the building. The common and jack rafters, as in 
any other roof, cross the plates at right angles. 

This roof creates several interesting framing prob- 

127 


128 


(COURSE IN ROOF FRAMING 


lems, which at first may appear difficult, although simple 
when once the basic principles are understood. 

Specifications. —Plate, long common side, %" x 2 1 /2". 

Plate, short common side, %" x 3%". 

Hip and valley rafters, %" x 1*4". 

Common and jack rafters, %" x 

Bulge, %"xl%". 

Projection, 2". 

Facia, 

Plancher level to plate level, short 
common rafters, 2%". 

Plancher level to plate level, long 
common rafters, 2". 

Pitch, long common rafters, 12" rise 
in one foot (V 2 pitch). 

Dimensions (see plan, Figure 55). 

Bafters spaced 2" on centers. 

Layout. —A full size working layout of the plan, 
Figure 55, should he drawn on a board or sheet of 
detail paper. The layout will represent a scale of 1" 
to the foot. In applying the various measurements full 
size substitute the word feet for inches in listing the 
runs and lengths of the rafters. Number each rafter 
and ridge as shown on the plan. Put the corresponding 
numbers on the rafters as they are laid out so as to 
insure ready identification and proper location during 
the erection of the roof. 

It will also be necessary to develop a profile of both 
the long and short common rafters on the layout as 
shown in Figure 56 so as to determine the proper 



HOW TO FRAME A ROOF OF UNEQUAL PITCH 


129 


heights of the walls or plate levels. First, draw a 
profile of the long common rafters, the specifications 
calling for a half pitch roof, or rafters rising 12" in 
one foot of run. In a half pitch roof, the run and the 
rise are the same, so if the run of the long common 
rafter is 11" (see plan, Figure 55) the total rise of the 



rafter must also he 11". With the total rise of the 
roof known, draw a profile of the short common rafter, 
the run of which, is 8", thus determining the pitch 
of the short common rafters. 

In accordance with the specifications, which give the 



















































































130 


COURSE IN ROOF FRAMING 


desired width of the facia and projection, locate the 
plate levels on either rafter. It will be discovered that 
if the plates on walls J, K and L which support the 
long common rafters were on the same level or height as 



the plates on walls M, N and 0 which support the short 
common rafters, the birdsmouth on the long 1 common 
rafters would almost cut the rafters in two. To over¬ 
come this difficulty the plates on walls J , K and L 












































































































HOW TO FRAME A ROOF OF UNEQUAL PITCH 


131 


which support the long common rafters are dropped 
sufficiently to get a good seat cut on the plates and yet 
to not weaken the rafter at the birdsmouth. With the 
birdsmoutlis developed independently on both the long 
and short common rafters, measure the height of each 
plate level from the plancher level and subtract the two 
figures, which will give the difference in the heights of 
the two plate levels, %", the plancher level being level 
throughout the entire roof. 

To Lay Out the Long Common Rafter .—The pitch 
of long common rafters No. 16 required by the specifi¬ 
cations is 12" rise in one foot. The run is taken from 
the layout, Figure 55, measuring from the facia line to 
center line of ridge D, A-C, or 11". Set the fence and 
square at 12" rise on the tongue and 12" run on the 
blade. Mark on the tongue for all plumb cuts and on 
the blade for all level cuts. Press the fence firmly 
against the top edge of the stock to be used and pro¬ 
duce the facia line or first plumb line to the extreme 
right, A, Figure 57. Slide the fence to the left and 
measure on a level line from facia line A the run of the 
rafter, 11", and produce plumb line C, Figure 57, the 
extreme length of the rafter to the center line of ridge 
L). From this length deduct one-half the thickness of 
the ridge, 3/16", and produce plumb line D, the cutting 
length of the rafter against the ridge. 

To complete the lay-out of the lower end of the rafter 
measure in from facia line A, measuring on a level line, 
2", the width of the projection, locating wall line B. 
Measure down on facia line A from the top edge of the 


132 


COURSE IN ROOF FRAMING 


rafter, the width of the facia, locating* plancher 

level F. Measure up from plancher level F, measuring 
on a plumb line, 2" (take this distance from the layout, 
Figure 56) locating plate level G. Cut on line A for the 



Figure 57.—Developed Length of Long Common Rafter No. 16 


facia, on line F for the plancher level, on lines G and B 
for the birdsmoutli and on line D for the cut against the 
ridge. 

To Lay Out Jack Rafters on Long Common Side .— 
The lengths of jack rafters Nos. 12, 13, 14 and 15 are 

















HOW TO FRAME A ROOF OF UNEQUAL PITCH 


133 


determined in the same manner as for the preceding 
common rafter No. 16, since they are a part of the 
length of it. Take the runs from the layout, Figure 55, 
measuring from facia line A to the center of the hip. 



The four rafters are shown developed on the side of 
a. single rafter, Figure 58. In practice these would be 
laid out separately hut are here laid out over one an¬ 
other to save space and to avoid repetition. Press the 













































134 


COURSE IN ROOF FRAMING 


fence firmly against the top edge of the stock to be 
used, using the same figures on the square as for the 
previous rafter, and produce the facia line or first 
plumb line to the extreme right, A, Figure 58. Slide the 
fence to the left and measure on a level line from facia 
line A the run of rafter No. 12, 2%"; the run of rafter 
No. 13, 5%"; the run of rafter No. 14, 8 %"; the run of 
rafter No. 15, 11"; and produce plumb line C, Figure 58, 



Figure 59.—Full Size Section Through W-W Figure 55, Showing Inter¬ 
section of Jack and Hip Rafters on the Long Common Side 


the extreme length of the rafter to the center line of 
the hip rafter. From this length deduct one-lialf the 
thickness of the hip measured on the line of the jack 
rafter, or one-half the diagonal thickness of the hip, 
C D, Figure 59, which is an enlarged section through 
W-W, Figure 55, and produce plumb line D, Figure 58. 
Square this line, across the top edge of the rafter and 
locate the center. 

To simplify picking up the bevel for the top cut, draw 
in a section of the hip and jack rafter, full size, oil 










HOW TO FRAME A ROOF OF UNEQUAL PITCH 


135 


the layout, Figure 55, as shown in the section, Figure 
59. Where the outside edges of the jack rafter inter¬ 
sect the outside edge of the hip rafter, square a line 
across at right angles to the center line until it inter¬ 
sects the center line as at 1 , Figure 59. 

To lay out the top cut so that the jack rafters will fit 
against the side of the hip rafter at the proper angle, 
measure back on a level line from plumb line D, on the 
side of the rafter, Figure 58, the distance D-l, Figure 
59, and produce plumb line 7, Figure 58. Connect 
plumb line 1 through plumb line D on the center line 
as shown at 2, top view, Figure 58. The lower end of 
the rafter is a duplicate of the long common rafter. 
Measure in from facia line A, measuring on a level line, 
2", the width of the projection, locating wall line B. 
Measure down on facia line A, from the top edge of 
the rafter, %", the width of the facia, locating planclier 
level F. Measure up from planclier level F, measuring 
on a plumb line, 2", locating plate level G. Cut on line 
A for the facia, on line F for the planclier level, on 
lines G and B for the birdsmouth and on bevel 2 on the 
top edge and plumb line 1 for the cheek cut against the 
hip rafter. 

The lengths of jack rafters Nos. 17, 18, 19 and 20 
are determined in the same manner as for the preceding- 
jack and common rafters, with the exception that the 
top and bottom cuts are different. Take the runs from 
the layout, Figure 55, measuring from the center of 
the ridge to the center of the valley rafter. The four 
rafters are shown developed on the side of a single 
rafter, Figure 60. In practice these would be laid out 


136 


COURSE IN ROOF FRAMING 


separately but are here laid out over one another to 
save space and to avoid repetition. Press the fence 
firmly against the top edge of the stock to be used and 



Figure 60.—Developed Length of Jack Rafters Nos. 17, 18, 19 and 20 

produce the first plumb line to the extreme right, C, 
Figure 60. Slide the fence to the left and measure on a 
level line the run of rafter No. 17, 11"; the run of 
rafter No. 18, 8*4”; the run of rafter No. 19, 5 y 2 " and 






























































HOW TO FRAME A ROOF OF UNEQUAL PITCH 


137 


the run ot rafter No. 20, 2%"; and produce plumb line C, 
Figure 60, the extreme length of the jack rafters to the 
center line of the ridge. From this length deduct one- 
halt the thickness of the ridge, 3/16", and produce plumb 
line D, the cutting length of the rafter against the ridge. 

The bottom ends of all four rafters are beveled to 
make a fit against the side of the valley, and jack rafter 
No. 17 also has a bearing on the plate so that the 
plancher level and birdsmouth must be laid out as for 
the common rafter. To lay out the birdsmouth for 
rafter No. 17, measure in from plumb line A, Figure 60, 
measuring on a level line, 2", the width of the projection, 
locating wall line B. Measure down on plumb line A, 
from the top edge of the rafter, the width of the 
facia, locating plancher level F. Measure up from 
plancher level F, 2", measuring on a plumb line, locating 
plate level G. Plumb line A represents the extreme 
length of the jack rafters to the center line of the valley 
rafter, so from this length deduct one-half the thickness 
of the valley measured on the line of the jack rafter, or 
one-half the diagonal thickness of the valley, C-D, 
Figure 59, which is an enlarged section through W-W, 
Figure 55, and produce plumb line D. Square this line 
across the top edge and locate the center. 

The top cuts for these rafters are the same as for 
the preceding jack rafter, as all rafters on the long 
common side of the hip and valley rafters are the same 
pitch. To lay out the top cut so that the jack 
rafters will fit against the side of the valley rafter at 
the proper angle measure forward on a level line from 
plumb line D, on the side of the rafter, Figure 60, the 


138 


COURSE IN ROOF FRAMING 


distance D-1, Figure 59, and produce plumb line 1, 
Figure 60. Connect plumb line 1 through plumb line B 
on the center line as shown at 2, top view, Figure 60. 
Cut on line D for the cut against the ridge and on bevel 
2 on the top edge and plumb line 1 for the cheek cut 
against the valley rafter on all four rafters. On rafter 
No. 17 only, cut on line F for the planclier level and 
on lines G and B for the birdsmoutli. 

To Lay Out Short Common Rafters. —Before setting 
the fence and square, the pitch, or rise in inches per 
foot, must be determined. The run, a constant unit, 
12", remains unchanged. The run of short common 
rafter No. 6 measured on the layout, Figure 55, measur¬ 
ing from the facia line to the center of the ridge C, A-C y 
is 8". The total height from the top of the facia to the 
top of the ridge is 11". This height is determined by 
the pitch of the long common rafters as required by 
the specifications and gives the total height of the roof. 
Thus, with the total rise 11" and the total run 8", find 
the rise in inches per foot. 

Formula: 

Rise in inches . . . 7 , , 

— -t—t- -—rise in inches per toot. 

Run in feet 

Working this out as given in the problem, we have: 

11/8 x 12/1 16 1/2" = rise in inches per foot. 

Set the fence and square at 1614" rise on the blade 
and 12" run on the tongue. Mark on the blade for all 
plumb cuts and on the tongue for all level cuts. Press 
the fence firmly against the top edge of the stock to be 




fflTE 


HOW TO FRAME A ROOF OF UNEQUAL PITCH 


139 


























140 


COURSE IN ROOF FRAMING 


used and produce the facia line or first plumb line to 
the extreme left, A, Figure 61. Slide the fence to the 
right and measure on a level line from facia line A 
the run of the rafter, 8", and produce plumb line C, 
Figure 61, the extreme length of the rafter to the center 
line of ridge C. From this length deduct one-half the 
thickness of the ridge, 3/16", and produce plumb line D, 
the cutting length of the rafter against the ridge. 

To complete the layout of the lower end of the rafter 
measure in from facia line A, measuring on a level 
line, 2", the width of the projection, locating wall line B. 
Measure down on facia line A from the top edge of the 
rafter, the width of the facia, locating plancher 

level F. Measure up from plancher level F, measuring 
on a plumb line, 2%" (take this distance from the lay¬ 
out, Figure 56, noticing that the short common rafters 
rest on plates M and 0 which are %" higher than plates 
J and L on which the long common rafters rest) locating 
plate level G. Cut on line A for the facia, on line F 
for the plancher level, on lines G and B for the birds- 
moutli and on line D for the cut against the ridge. 

To Lay Out Jack Rafters on Short Common Side .— 
The lengths of jack rafters Nos. 1, 2, 3, 4 and 5 are 
determined in the same manner as for the preceding 
common rafter No. 6, since they are a part of the length 
of it. Take the runs from the layout, Figure 55, 
measuring from the facia line to the center of the hip 
rafter. The five rafters are shown developed cn the 
side of a single rafter, Figure 12. In practice these 
would be laid out separately but are here laid out over 
one another to save space and to avoid repetition. Press 


HOW TO FRAME A ROOF OF UNEQUAL PITCH 141 



End View 

Figure 62.—Developed Length of Jack Rafters Nos. 1, 2, 3, 4 and 5 















































































142 


COURSE IN ROOF FRAMING 


the fence firmly against the top edge of the stock to 
be used, using the same figures on the square as for 
the previous rafter, and produce the facia line or first 
plumb line to the extreme left, A, Figure 62. Slide the 
fence to the right and measure on a level line from facia 


line A the run of rafter No. 



12 ’ 


the run of 


rafter No. 2, 2 


; the run of rafter No. 3, 4— 


the run of rafter No. 4, 5 3/4"; and the run of rafter 
■ 2 %" 


No. 5, 7- 


12 


and produce plumb line (7, Figure 62, 


the extreme length of the rafter to the center line of 
the hip rafter. From this length deduct one-lialf the 
thickness of the hip, measured on the line of the jack 
rafter, or one-lialf the diagonal thickness of the hip, 
C-D, Figure 63, which is an enlarged section through 
U-U, Figure 55, and produce plumb line D. Square this 
line across the top edge of the rafter and locate the 
center. 

To simplify picking up the bevel for the top cut, 
draw in a section of the hip and jack rafter, full size, 
on the layout, Figure 55, as shown in the section, Figure 
63. Where the outside edge of the jack rafter intersects 
the outside edge of the hip rafter square a line across 
at right angles to the center line until it intersects the 
center line as at 1 , Figure 63. 

To lay out the top cut so that the jack rafters will tit 
against the side of the hip rafter at the proper angle 
measure back on a level line from plumb line D on the 
side of the rafter, Figure 62, the distance D-l, Figure 






HOW TO FRAME A ROOF OF UNEQUAL PITCH 


143 


63, and produce plumb line 1, Figure 62. Connect plumb 
line 1 through plumb line 1) on the center line as shown 
at 2, top view, Figure 62. The lower end of the rafter 
is a duplicate of the short common rafter. Measure in 
from facia line A, measuring on a level line, 2", the 
width of the projection, locating wall line B. Measure 



down on facia line A from the top edge of the rafter, 
the width of the facia, locating plancher level F. 
Measure up from plancher level F, measuring on a 
plumb line, 2%", locating plate level G. Cut on line A 
for the facia, on line F for the plancher level, on lines 
G and B for the birclsmoutli and on bevel 2 on the 
top edge and plumb line 1 for the cheek cut against the 
hip rafter. 

The lengths of jack rafters Nos. 7, 8, 9, 10 and 11 
are determined in the same manner as for the preceding 
jack and common rafters, with the exception that the 









144 


COURSE IN ROOF FRAMING 



Figure 64.—Developed Length of Jack Rafters Nos. 7, 8, 9, 10 and 11 
























































HOW TO FRAME A ROOF OF UNEQUAL PITCH 


145 


top and bottom cats are different. Take the runs from 
the layout, Figure 55, measuring from the center of 
the ridge to the center of the valley rafter. The four 
rafters are shown developed on the side of a single 
rafter, Figure 64. In practice these would be laid out 
separately but are here laid out over one another to 
save space and to avoid repetition. Press the fence 
firmly against the top edge of the stock to be used and 
produce the first plumb line to the extreme left, C, 
Figure 64. Slide the fence to the right and measure on 
a, level line the run of rafter No. 7, 8"; the run of 

rafter No. 8, 6 1/2"; the run of rafter No. 9, 5-——; the 


run of rafter No. 10, 



and the run of rafter 


No. 11, 2 



and produce plumb line C, Figure 64, the 


extreme length of the jack rafters to the center line of 
the ridge. From this length deduct one-half the thick¬ 
ness of the ridge, 3/16", and produce plumb line D, the 
cutting length of the rafters against the ridge. 

The bottoms of all five rafters are beveled to make a 
fit against the side of the valley. Jack rafters Nos. 7 
and 8 also have a bearing on the plate so that the 
plancher level and birdsmouth must be laid out on 
common rafter No. 7 and the birdsmouth only 
on rafter No. 8. To lay out the birdsmouth for 
rafters Nos. 7 and 8 measure in from plumb line A, 
Figure 64, measuring on a level line, 2", the width of 
the projection, locating wall line B. Measure down on 
plumb line A, from the top edge of the rafter, %", the 





146 


COURSE IN ROOF FRAMING 


width of the facia, locating plancher level F. Measure 
up from plancher level F, 2%", measuring on a plumb 
line, locating plate level G. Plumb line A represents the 
extreme length of the jack rafters to the center line of 
the valley rafter, so from this length deduct one-half 
the thickness of the valley measured on the line of the 
jack rafters or one-half the diagonal thickness of the 
valley, C-D, Figure 63, which is an enlarged section 
through U-U, Figure 55, and produce plumb line D, 
Figure 64. Square this line across the top edge and 
locate the center. 

The bottom cut for these rafters is the same as for 
the preceding jack rafters, as all rafters on the short 
common side of the hip and valley rafters are the same 
pitch. To lay out the bottom cut so that the jack rafters 
will fit against the side of the valley rafter at the proper 
angle measure forward on a level line from plumb line 
D, on the side of the rafters, Figure 64, the distance D-l, 
Figure 63, and produce plumb line 1, Figure 64. Con¬ 
nect plumb line 1 through plumb line D on the center 
line as shown at 2, top view, Figure 64. Cut on line D 
for the cut against the ridge and on bevel 2 on the top 
edge and plumb line 1 for the cheek cut against the 
valley rafter on all five rafters. On rafters Nos. 7 and 
8 cut on lines G and B for the birdsmouth. On rafter 
No. 7 cut on line F for the plancher level. 

To Lay Out the Hip Rafter .—The hip rafter travels 
the diagonal distance of an oblong with reference to the 
plates of a building, this being due to the fact that the 
roof surface on one side of the hip rafter has a greater 
pitch than the roof surface on the opposite side. The 



HOW TO FRAME A ROOF OF UNEQUAL PITCH 


147 


top edges of all rafters must be in alignment to receive 
the roof boards. The plancher level should be level 
throughout the entire roof. The outside lines of the 
roof that are seen, or the facia lines, must intersect. 

Refering to Figure 66, an enlarged section through 



R-R, Figure 55, it will readily be seen that the hip 
rafter traveling the diagonal distance of an oblong and 
intersecting with the return corner on the facia line 
crosses the plate at an angle A-R, Figure 66. In roots 
of equal pitch the hip rafter only crosses the corner of 
a building where the roof surfaces on both sides of 




















148 


COURSE IN ROOF FRAMING 


the hip are the same pitch and the hip travels the 
diagonal distance of a square or crosses the plates of a 
building at an angle of forty-five degrees. 

In all roofs of equal pitch the run of the hip rafter 
is 17" for every foot of run of the common rafter, or 
the diagonal distance of 12" and 12". This rule cannot 



Figure 66.—Full Size Section Through R-R, Figure 55, Showing Inter¬ 
section of the Hip Rafter Plate and Facia Line 

apply in roofs of unequal pitch because the hip rafter 
runs the diagonal distance of an oblong, therefore it 
becomes necessary to determine the rise in inches per 
foot of run so that the constant unit of 12" can be 
used in framing all the rafters throughout the entire 
roof. 

The total ri se of the hip rafter is determined by the 









HOW TO FRAME A ROOF OF UNEQUAL PITCH 


149 


pitch of the long common rafter, which is one-half pitch 
as noted in the specifications. In a half pitch roof the 
run and rise are the same. If the common rafter rises 
12" in one foot, it rises 11" in 11". The run of the 
long common rafter being 11", the total rise must also 
be 11", which is the extreme height of the roof. 

Take the run of the hip rafter from the layout, Figure 
55, measuring from the return on the facia line to the 
butt joint against the valley rafter, A-T, Figure 55, or 


a run of 13—^". 

12 

total run of 13—- 

12 


Thus, with a total rise of 11" and a 
", find the rise in inches per foot of 


run. 


R ise in inches 


= rise in inches per foot. 


Run in feet 

Working this out as given in the problem, we have: 


132 


13- 


7 % 


= 132 -f- 


12 


8 


= 132 x —- ) 4 = 9—" = rise in 
163i/ 4 12 12 


12 

inches per foot. 


Another way to determine the rise in inches per foot 
is shown in Figure 67. The same reading should be 
obtained provided the triangle has been laid out ac¬ 
curately. It is good practice to check up the figures 
with the steel square to avoid errors. Lay off the run 


on a horizontal line, 13—14 

12 


rr 


and the rise on a vertical 


line, 11". Connect the two lines with a diagonal line, 











150 


COURSE IN ROOF FRAMING 


forming a triangle. Measure off on the horizontal or 
level line from the intersection of the horizontal and 
diagonal lines the unit for one foot run, 12". Project 
a vertical or plumb line up from this point until it 
intersects the diagonal pitch line. The length of this 



Figure 67.—A Simple Method of Finding the Rise in Inches Per Foot of 

Run 


vertical line from the horizontal base line to the diagonal 
pitch line is the rise in inches per foot of the rafter, 
or 9 8/12". 

Set the fence and square at 9 8/12" rise on the tongue 
and 12" run on the blade. Mark on the tongue for all 















HOW TO FRAME A ROOF OF UNEQUAL PITCH 


151 


plumb cuts and on the blade for all level cuts. Press 
the fence firmly against the top edge of the stock to 
be used and produce the facia line or first plumb line 
to the extreme left, A, Figure 65. Slide the fence to 
the right and measure on a level line from facia line A 


the run ol the hip, and produce plumb line T, 

JL -j 

Figure 65, the extreme length of the rafter forming the 
butt joint against the valley rafter. 

To simplify picking up the bevels for the top cut, the 
backing and other measurements required in laying out 
the hip rafter, draw in a section of the hip rafter and 
plate, full size, on the layout, Figure 55, as shown in 
the section, Figure 66, which is a section through R-R, 
Figure 55. Where the outside edges of the hip rafter 
intersect the facia line square lines across at right 
angles to the center line from both edges of the hip 
until they intersect the center line as at 1 and 2, Figure 
66. Also, where the outside edge of the hip intersects 
the wall line, square a line across at right angles to the 
center line until it intersects the center line as at 3, 
Figure 66. 

To complete the layout of the lower end of the hip 
rafter measure in on a level line the diagonal distance 
of the projection A-B, Figure 66, from facia line A, on 

° locating wall line R, 


the side of the rafter, or 


12 


Figure 65. Square this line across the bottom edge of 
the rafter and locate the center point. To make a fit 
against the wall at the proper angle, measure in on the 
side of the rafter from wall line B the distance B-3 , 




152 


COURSE IN ROOF FRAMING 


Figure 66, and produce plumb line 3 , Figure 65. Con¬ 
nect plumb line 3 through the center of plumb line B 
on the bottom edge as shown at 4, bottom view, Figure 
65. To complete the birdsmoutli measure down on facia 
line A from the top edge of the rafter, the width 
of the facia, and produce plancher level F. Measure 
up from plancher level F on a plumb line 2%", locating 
plate level G. The hip rafter crosses plate 0 , the same 
plate upon which the short common rafters rest; there¬ 
fore, the distance between plancher level and plate level 
is the same for short common jack rafters, short com¬ 
mon rafters and hip rafter. 

To make the return on the facia line at the corner of 
the building measure back on side A of the hip rafter 
from facia line A the distance A-l, Figure 66, and pro¬ 
duce plumb line 1, Figure 65. On side B measure back 
on a level line from facia line A the distance A-2, 
Figure 66, and produce plumb line 2, Figure 65. Square 
facia line A across the top edge of the rafter and locate 
the center point. Connect plumb lines 1 and 2 on the 
side of the rafter with the center point on the top edge 
as shown in the top view at 5. Figure 65. Cut on bevels 
5 on the top edge and plumb lines 1 and 2 on the side 
of the rafter for the facia and on line F for the plancher 
level. On line G make a square cut and on bevel 4 and 
on plumb line B on the bottom edge of the rafter make 
a bevel cut for the birdsmoutli, also on line T for the 
butt joint against the valley rafter. 

To Bach the Hip Rafter .—To determine the amount 
of stock to be removed in beveling the corners of the 
hip to bring the center line in alignment with the center 



HOW TO FRAME A ROOF OF UNEQUAL PITCH 


153 


line of the jack and common rafters produce a level 
line on either side of the hip. On side A, from the top 
edge on this level line, point off the distance A-l, 
Figure 66, as shown at A-l , Figure 65. On side B, 
from the top edge on the level line point off the distance 
A-2, Figure 66, as shown at A-2, Figure 65. Gauge a 
line through these points on either side of the rafter and 
also through the center on the top edge. Remove the 
corner between these lines as shown in the end view, 
Figure 65. 

To Lay Out the Valley Rafter .—The length of the 
valley rafter is determined in the same manner as that 
of the preceding hip rafter. Take the run from the lay¬ 
out, Figure 55, measuring from the return on the facia 
line to the butt joint against the hip rafter, A-T, Figure 


14, or 1 



Press the fence firmly against the top 


edge of the stock to be used and produce the facia line 
or first plumb line to the extreme right, A, Figure 68. 
Slide the fence to the left and measure on a level line 


from facia line A the run of the hip, 13^1", and pro- 

12 

duce plumb line T, Figure 68, the extreme length of the 
rafter forming the butt joint against the hip rafter. 

To simplify picking up the bevels, the top cut and 
other measurements required in laying out the valley 
rafter, draw in a section of the valley and plate, full 
size, on the layout, Figure 55, as shown in the section 
Figure 69, which is a section through S-S, Figure 55. 
Where the center lines of the valley rafter intersect the 
facia line square a line across at right angles to the 



154 


COURSE IN ROOF FRAMING 


center line, intersecting both edges of the valley as at 
A-A, Figure 69. Also, where the outside edge of the 
valley intersects the wall line square a line across at 
right angles to the center line until it intersects the 



Figure 68.—Developed Length of the Valley Rafter 

center line as at 3 , Figure 69. 

To complete the layout of the lower end of the valley 
measure in on a level line from facia line A the diag¬ 
onal distance of the projection A-B, Figure 69, on the 






















HOW TO FRAME A ROOF OF UNEQUAL PITCH 155 

side of tile rafter, or 2Vo", locating wall line B, Figure 
68. Square this line across the bottom edge of the 
rafter and locate the center point. To make a fit against 



the wall at the proper angle measure in on the side of 
the rafter from wall line B the distance B-3, Figure 69, 
and produce plumb line 3, Figure 68. Connect plumb 




















156 


COURSE IN ROOF FRAMING 


line 3 through the center of plumb line B on the bottom 
edge as shown at 4 , bottom view Figure 68. 

To complete the birdsmouth measure down on facia 
line A from the top edge of the rafter %", the width of 
the facia, and produce plancher level F. Measure up 
from plancher level F on a plumb line 2", locating 
plate level G. 

The valley rafter crosses plate L, the same plate upon 
which the long common rafters rest; therefore, the dis¬ 
tance between plancher level and plate level is the 
same for the long common jack rafters, long common 
rafters and for the valley rafter. 

To make the return on the facia line at the corner 
of the building measure forward on side A of the valley 
rafter from facia line A the distance A-l, Figure 69, and 
produce plumb line 1, Figure 68. On side B measure 
forward on a level line from facia line A the distance 
A-2, Figure 69, and produce plumb line 2, Figure 68. 
Square facia line A across the top edge of the rafter 
and locate the center point. Connect plumb lines 1 and 
2 on the side of the rafter with the center point on the 
top edge as shown in the top view at 5, Figure 
68. Cut on bevels 5 on the top edge and plumb lines 
1 and 2 on the side of the valley for the facia. Cut on 
line F for the plancher level. On line G make a square 
cut and on plumb line B, bevel 4 on the bottom edge of 
the rafter a bevel cut for the birdsmouth and on line T 
for the butt joint against the hip rafter. 

To Lay Out the Bulges .—The run of the ridges is 
taken from the layout, Figure 55. For ridge C measure 
the extreme length from the facia line to the intersection 


HOW TO FRAME A ROOF OF UNEQUAL PITCH 


157 


oi the center line oi‘ the hip and valley rafters and the 
ridge. From this length deduct one-half the thickness 
ot the valley rafter measured on the line of ridge C or 
one-half the diagonal thickness of the valley, T-W, 
h iguro 70, and locate the center on the top edge. Set 
a bevel scjuare on the layout to the angle formed by the 
intei section ot the valley and ridge. .Apply the 
bevel on the top edge of the ridge and draw a line 
through the center point thus obtained. For ridge D 



Figure 70. Full Size Section Through V-V, Figure 55, Showing Inter¬ 
section of the Hip and Valley Rafters and the Ridge 


measure the extreme length from the facia line to the 
intersection of the center line of the hip and valley 
rafters and ridge. From this length deduct one-half 
the thickness of the hip rafter measured on the line of 
ridge D or one-half the diagonal thickness of the hip 
T-W, Figure 70, and locate the center point. Set a 
bevel square on the layout at the angle formed by the 
intersection of the hip and ridge D. Apply the bevel 
on the top edge of the ridge and draw a, line through 
the center point thus obtained. 

To Assemble the Roof .—Assemble the rafters as 
shown in the elevation, Figure 71. Set up and fasten 







158 


COURSE IN ROOF FRAMING 


the hip and valley rafters first. The center lines of 
both rafters must intersect at the apex. Set up ridges 
C and D, securing them in place at the proper height 
by a pair of common rafters. The top edges of the 
ridges are kept flush with the top edges of the common 



Figure 71.—Elevation of Unequal Pitch Roof, Showing Method of 

Framing the Rafters 

rafters. This drops the ridge out of its normal posi¬ 
tion, prevents the need for backing the ridge and thus 
throws the top edge out of alignment with the top 
edges of the hip and valley rafters. 

Both ridges are not on the same level. One ridge is 
lower than the other owing to the steeper pitch. If 




HOW TO FRAME A ROOF OF UNEQUAL PITCH 


159 


tlie ridges were backed to the pitch of the roof and the 
lines of the common rafters were continued to the 
extreme point, all lines would terminate in alignment 
with the extreme high point formed by the intersection 
of the hip and valley rafters. The roof hoards con¬ 
tinue these lines up so that when the roof is completed 
all roof surfaces are in alignment. 

The exact location of the ridges where they intersect 
the hip and valley rafters may he determined by their 
location with reference to the butt joint of the hip and 
valley. Draw in a section of the hip, valley and ridge, 
full size on the layout, Figure 55, as shown in the 
section, Figure 70, which is a section through V-V T 
Figure 55. Square a line across at right angles to the 
center line of the hip at the intersection of the hip and 
valley rafter, as at R, Figure 70, thus establishing the 
butt joint between the two rafters. The distance R-S T 
Figure 70, gives the distance between the butt joint and 
the long point of the bevel of the ridge on the side of 
the rafter. 

Development of the Rafters on the Plan .—Figure 72 
will serve to illustrate and prove the lengths and bevels 
and will explain in a graphic way how they are ob¬ 
tained. 

A to B is the rise of the long common rafter. 

A to C is the rise of the short common rafter. 

A to D is the run of the long common rafter. 

A to E is the run of the short common rafter. 

R to D is the length of the long common rafter. 

C to E is the length of the short common rafter. 


160 


COURSE IN ROOF FRAMING 



Figure 72.—Graphic Method of Developing the Lengths and Bevels 
the Various Rafters Used in Framing an Unequal Pitch Roof 































HOW TO FRAME A ROOF OF UNEQUAL PITCH 


161 


D to F is the developed length of the long common 
rafter. 

E to G is the developed length of the short common 
rafter. 

A to H is the rise of the hip and valley rafter. 

A to / is the run of the hip and valley rafter. 

H to / is the length of the hip and valley rafter. 

F to 1 and G to 1 are the developed lengths of the 
hip rafter. 

A to J and A to K are the developed lengths of the 
valley rafter. 

P to Q shows the developed lengths of iack rafters 
1, 2, 3, 4 and 5. 

Angle L gives the top cut for jack rafters 1, 2, 3, 4 
and 5. 

R to S shows the developed lengths of jack rafters 
8, 9, 10 and 11. 

Angle M gives the top cut for jack rafters 8, 9, 10 
and 11. 

T to U shows the developed lengths of jack rafters 
12, 13 and 14. 

Angle N gives the top cut for jack rafters 12, 13 
and 14. 

V to W is the developed length of jack rafters 18, 19 
and 20. 

Angle 0 gives the top cut for jack rafters 18, 19 
and 20. 

Runs and Lengths of Rafters .—The following table is 
prepared to assist the student in checking up his work. 
It is intended that the framer will take his runs from 
the layout and develop the lengths with the steel square 



162 


course: in roof framing 


and fence, using the tables only as a matter of in¬ 
formation to give him assurance that lie has taken the 
proper runs and determined the correct lengths of the 
rafters. The measurements listed in the table are the 
extreme lengths on the center lines. Make allowances 
where rafters intersect a ridge, hip or valley rafter for 
the cutting lengths. It is suggested that the reader 
frame a model of the roof for practice, building it to 
the same scale as the layout, 1" to the foot. In using 
the table to check the model, read feet as inches; for 

5 % 


example, on rafter No. 1, the run would read 1 


12 


The square being laid out in 


and the length 2—^-". 

12 

twelfths of an inch it is an easy matter to check the 
work up accurately. 


RUNS AND LENGTHS OF RAFTERS USED IN FRAMING ROOF 

OF UNEQUAL PITCH 


Number of 
Rafters 

Quantity of 
Rafters 

Runs 

Lengths 

Kind of Rafters 

1 

1 

1' 51/4" 

2' 5*4" 

Jack Rafters on 
Short Common 
Side 

2 

1 

2'ioy 2 " 

3' 2*4" 

Jack Rafters on 
Short Common 
Side 

3 

1 

4' 3%" 

7' 4" 

Jack Rafters on 
Short Common 

4 

1 

5' 9" 

9' 9%" 

Side 

Jack Rafters on 

5 

1 

r 2 ye' 

12' 2%" 

Short Common 
Side 

6 

12 

8' 0" 

13' 7*4" 

Short Commons 
Jack Rafters on 

7 

1 

8' 0" 

13' 7*4" 

Short Common 
Side 

8 

1 

6' 6" 

11' 0%" 

Jack Rafters on 
Short Common 
Side 
























HOW TO FRAME A ROOF OF UNEQUAL PITCH 163 


RUNS AND LENGTHS OF RAFTERS USED IN FRAMING ROOF 

OF UNEQUAL PITCH 


Number of 
Rafters 

Quantity of 
Rafters 

Runs 

Lengths 

Kind of Rafters 

9 

1 

5' 0%" 

8 ' 714 " 

Jack Rafters on 
Short Common 
Side 

10 

1 

3' 7y 2 " 

6' 1%" 

Jack Rafters on 
Short Common 

11 

1 

2 ' 2VI" 

3' 8%" 

Side 

Jack Rafters on 

12 

1 

2' 9" 

3'10%" 

Long Common 
Side 

13 

1 

5' 6" 

7' 9%" 

Jack Rafters on 
Long Common 

14 

1 

8' 3" 

11' 0" 

Side 

Jack Rafters on 

15 

1 

11' 0" 

15' 6Vs" 

Long Common 
Side 

16 

10 

11' 0" 

15' 6%" 

Long Commons 
Jack Rafters on 

17 

1 

11' 0" 

15' 65/s" 

Long Common 
Side 

18 

1 

8' 3" 

11' 8" 

Jack Rafters on 
Long Common 

19 

1 

5' 6" 

7' 9%" 

Side 

Jack Rafters on 

20 

1 

2' 9" 

3'10%" 

Long Common 
Side 

A 

1 

13' 714" 

17' 6" 

Hip Rafter 

B 

1 

13' 71/i" 

17' 6" 

Valley Rafter 

C 

1 

17' O" 

17' 0" 

Ridge 

D 

1 

14' 0" 

14' 0" 

Ridge 


Figures to use on tlie steel square: 

Long common rafters, 12" on tongue and 12" on blade. 
Mark on the tongue for plumb cut and on blade for 
level cut. 

Short common rafters, 16%" on tongue and 12" on 
blade. Mark on tongue for level cut and on blade for 
plumb cut. 

Hip and valley rafters 9 8/12" on tongue and 12" on 
blade. Mark on tongue for plumb cut and on blade for 
level cut. 



















CHAPTER VI 


AN ADVANCED PROBLEM IN FRAMING AN UNEQUAL PITCH 
ROOF WITH DORMERS—PROBLEM 8 

The main roof and dormers S and W pitch 12" in 
one foot while dormers T and U only pitch 6" in one 
foot. Dormer U intersects with a gable, forming an 
unequal pitch roof or the intersection of two roofs of 
different pitches, one roof one-lialf pitch and the other 
roof one-fourtli pitch. The general principles involved 
in framing the main rafters are the same as those 
described in the preceding chapters dealing with roofs 
of equal pitch. The method of framing the rafters for 
dormer U is the same as that described in Chapter V 
dealing with roofs of unequal pitch. 

Specifications. —Plate, %" x 2". 

Hip and valley rafters, %" x 1*4". 

Common and jack rafters, %" x 

Ridge, %" x !%". 

Projection: main roofs, 2"; dormers, 
1 ". 

Facia: main roof, y 2 "; dormers, y 2 ". 

Plancher level to plate level: main 
roof, 1 %"; dormers, S and W, 1"; 
dormers T and U, l / 2 "- 

Pitch: main roof and dormers S and 
W, 12" rise in one foot (y 2 pitch); 
dormers T and U, 6" rise in one 
foot (14 pitch). 

164 


DORMER 


FRAMING AN UNEQUAL PITCH ROOF WITH DORMERS 165 



Figure 73.—Plan of Problem 8, from Which the Working Layout Is Made 


56 










































































































































166 


COURSE IN ROOF FRAMING 


Dimensions (see plan, Figure 73). 

Rafters spaced 2" on centers. 

Layout .—A full size working layout of the plan, 
Figure 73, should he drawn on a board or a sheet of 
detail paper. The layout will represent a scale of 1" 
to the foot. In applying the various measurements full 
size, substitute the word feet for inches in listing the 
runs and lengths of the various rafters. 

To Lay Out Common Rafter No. 7 .—Set the fence 
and square at 12" rise on the tongue and 12" run on 
the blade. Mark on the tongue for all plumb cuts and 
on the blade for all level cuts. The run of rafter No. 7 
is taken from the layout, Figure 73, measuring from the 
facia line to the center of ridge L, or 10". Press the 
fence firmly against the top edge of the stock to be used 
and produce the facia or first plumb line to the extreme 
left, A, Figure 74. Slide the fence to the right and 
measure on a level line from facia line A the run of 
common rafter No. 7, 10", and produce plumb line C, 
Figure 74, the extreme length of the rafter to the center 
of the ridge. From this length deduct one-half the 
thickness of ridge L, 3/16", and produce plumb line D, 
the cutting length of the rafter against the ridge. 

To complete the layout of the lower end of the rafter 
measure in from facia line A, measuring on a level line 
2", the width of the projection, locating wall line B. 
Measure down on facia line A from the top edge of the 
rafter y 2 ", the width of the facia, locating plancher 
level F. Measure up from plancher level F, measuring 
on a plumb line 1%", locating plate level G. Cut on 


FRAMING AN UNEQUAL PITCH ROOF WITH DORMERS 167 


line A for the facia, on lines G and B for the birds- 
mouth and on line I) for the cut against ridge L. 

To Lay Out Jack Rafter No. 4 .—The jack rafters are 



Figure 74.—Developed Length of Common Rafter No. 7 


determined in the same manner as the preceding com¬ 
mon rafter since they are a part of the length of it. 
Take the run of jack rafter No. 4 from the layout, 
Figure 73, measuring from the facia line to the center 
















168 


COURSE IN ROOF FRAMING 


of hip A, or 8". Press the fence firmly against the top 
edge of the stock to be used and produce the facia line 
or first plumb line to the extreme left, A, Figure 75. 



Figure 75.—Developed Length of Jack Rafter No. 4 


Slide the fence to the right and measure on a level line 
from facia line A the run of rafter No. 4, 8", and 
produce plumb line C, the extreme length of the rafter 
to the center line of hip A. From this length deduct 
















FRAMING AN UNEQUAL PITCH ROOF WITH DORMERS 169 

one-liali the thickness of hip A measured on the line 
of the jack rafter, or one-half the diagonal thickness of 
the hip, y 2 " full, and produce plumb line D on the 
side of the rafter. Square this line across the top 
edge of the stock and locate the center point. 

-To lay out the top cut so that the jack will fit against 
the side of hip A at the proper angle measure forward 
on a level line from plumb line D a distance equal to 
one-half the thickness of the stock used for the jack 
rafter, 3/16", and produce plumb line 1. Connect plumb 
line 1 through plumb line D on the center line as shown 
at 2, top view Figure 75. 

The top cut can also be laid out with the steel square 
by using the length, 17" (bridge measure of the run 12" 
and the rise 12") on the blade and the run, 12", on the 
tongue. Mark on the blade for the top cut. The lower 
end of the jack rafter is a duplicate of the common 
rafter. Measure in from facia line A, measuring on a 
level line, 2", the width of the projection, locating wall 
line B. Measure down on facia line A from the top 
edge of the rafter %", the width of the facia, locating 
plancher level F. Measure up from plancher level F, 
measuring on a plumb line, 1%", locating plate level G. 
Cut on line A for the facia, on lines G and B for the 
birdsmoutli and on bevel 2 on plumb line 1 for the 
cheek cut against the side of hip A. 

To Lay Out Cripple Bafter No. 30 .—The cripple 
rafters are determined in the same manner as the preced¬ 
ing common rafter because they are a part of the length 
of it. Take the run of cripple rafter No. 30 from the 
layout, Figure 73, measuring from the center of hip K 


170 


COURSE IN ROOF FRAMING 


to the center of valley J, or 7". Press the fence firmly 
against the top edge of the stock to he used and pro¬ 
duce the first plumb line to the extreme left, C, Figure 



Figure 76.—Developed Length of Cripple Rafter No. 30 


76. Slide the fence io the right and measure on a level 
line from plumb line C the run of rafter No. 30, 7", 
and produce plumb line C, the extreme length of the 














FRAMING AN UNEQUAL PITCH ROOF WITH DORMERS 171 


rafter to the center of hip K and valley J. From this 
length deduct from either end one-lialf the thickness of 
the hip and valley measured on the line of the cripple 
rafter, or one-half the diagonal thickness of the hip and 
valley, y 2 " full, and produce plumb line D on either end 
of the rafter. Square these lines across the top edge of 
the stock and locate the center point. 

To lay out the top cuts so that the cripple rafter will 
fit against the side of the hip and valley at the proper 
angle measure forward on a level line from plumb 
lines D a distance equal to one-lialf the thickness of 
the stock used for the cripple rafter, 3/16", and produce 
plumb lines 1 on either end of the rafter. Connect 
plumb lines 1 through plumb lines D on the center line 
as shown at 2, top view Figure 76. 

These top cuts can also be laid out with the steel 
square by using the length 17" (bridge measure of the 
run 12" and the rise 12") on the blade and the run 12" 
on the tongue. Mark on the blade for the top cut. Cut 
on plumb lines 1 and bevels 2 for the cheek cut against 
the sides of hip K and valley J . 

To Lay Out Hip Rafter A .—Set the fence and square 
at 12" rise on the tongue and 17" run on the blade. 
Mark on the tongue for all plumb cuts and on the blade 
for all level cuts. The run of hip A is taken from 
the layout, Figure 73, measuring from the facia line 


to the center of ridge L, or 14 


1 %,/ 

12 ' 


Press the fence 


firmly against the top edge of the stock to be used and 
produce the facia line or first plumb line to the extreme 
left, A, Figure 77. Slide the fence to the right and 




172 


COURSE IN ROOF FRAMING 


measure on a level line from facia line A the run of 


the hip, 14 


12 


, and produce plumb line C, the extreme 


length of hip A to the center of ridge L. From this 
length deduct one-lialf the thickness of ridge L meas¬ 
ured on the line of hip A, or one-lialf the diagonal 



thickness of ridge L, 14", and produce plumb line D, 
Figure 77. Square this line across the top edge of the 
rafter and locate the center point. 

To lay out the top cut so that the hip rafter will tit 
against the side of ridge L measure forward on a level 
line from plumb line 7) a distance equal to one-half 



















FRAMING AN UNEQUAL PITCH ROOF WITH DORMERS 173 


the thickness of the stock used for the hip, and 
produce plumb line 1. Connect plumb line 1 through 
plumb line D on the top edge and produce bevel 2 as 
shown in the top view, Figure 77. 

This top cut can also be laid out with the steel 
square by using 10%" on the blade (one-half the bridge 
measure of the run 17" and the rise 12") and 8%" (one- 
lialf the run) on the tongue. Mark on the blade for the 
top cut. 

To complete the lower end of the rafter, measure in 
on a level line from facia line A the diagonal distance 
of the projection, 2" and 2", or 2 10/12", and produce 
wall line B. Measure down on facia line A from the 
top edge of the rafter %", the width of the facia, and 
joroduce plancher level F. Measure up from plancher 
level F on a plumb line 1%", locating plate level G. 

To make the return on the facia line at the corner 
of the building, square facia line A across the top edge 
of the hip and locate the center point. Measure in on 
a level line from facia line A, on either side of the 
rafter, a distance equal to one-lialf the thickness ot 
the stock used for the hip, %", and produce plumb line 
3. Connect plumb line 3 with the center point on the 
facia line as shown at 4, top view, Figure 77. This top 
cut is the same as the top cut at the upper end of the 
rafter. 

To determine the amount of backing so that the center 
line of the hip will come in alignment with the top edges 
of the common and jack rafters first gauge a line 
through the center of the rafter on the top edge. Then 
produce a level line anywhere on the side of the i after. 


174 


COURSE IN ROOF FRAMING 


On this level line measure off a distance equal to one- 
lialf the thickness of the stock used, from the top 
edge, as at M, Figure 77. Through this point gauge a 
line parallel with the top edge. Remove the corner of 
the stock between this line and the center line for the 
backing. Cut on line A on bevels 4 for the facia, on 
line F for the plancher level, on lines G and B for the 
birdsmouth and on plumb line 1 and bevel 2 for the 
joint against the side of ridge L. 

To Lay Out Bonner W .—The only new problem that 
arises in framing dormers is the proper height for the 
dormer plate. A simple method for determining this 
height is shown in Figure 78. The dormer is framed 
by the intersection of vallevs B and E. Valley D forms 
a tie between valley B and hip F and valley E forms 
a tie between valley B and the main plate, making a 
strongly constructed dormer. 

To determine the height of the dormer plate, first 
draw a profile of jack rafter No. 71, according to the 
specifications, as shown in Figure 78. Project the wall 
line up indefinitely. Parallel to this line draw the 
center line of ridge M, which is 3" from the center line 
of rafter No. 71. See layout, Figure 73. Produce a 
level line from the intersection of the top edge of rafter 
No. 71 and the wall line, Figure 78, and measure off 
on the center line of ridge M from this level line the 
run of ridge M taken from the layout, Figure 73, or 7", 
as shown in Figure 78. From this point draw the pitch 
of dormer rafter No. 70. With this line as the top 
edge of the rafter draw a profile of rafter No. 70 ac¬ 
cording to the specifications and determine the plate 



FRAMING AN UNEQUAL PITCH ROOF WITH DORMERS 17 5 



or 3 15/16", which gives the height of the dormer plate 










































176 


COURSE IN ROOF FRAMING 


above the level of the main plate, Figure 78. The length 
of the rafters is determined with the steel square and 
fence in a manner similar to those for the main roof. 



Figure 79.—Dormer S, Showing Method of Determining the Doimer 

Plate Level 

To Lay Oiit Dormer S .—Dormer S is similar to 
dormer W as previously described. The dormer is 
framed by the intersection of valleys I and J. Valley J 





































FRAMING AN UNEQUAL PITCH ROOF WITH DORMERS 177 


forms a tie with the plate and hip H, and valley / 
forms a tie with the plate and valley J. 

To determine the height of the dormer plate, draw 
a profile of jack rafter No. 35, according to the specifi¬ 
cations, as shown in Figure 79. Project the wall line 
up indefinitely. Parallel to this line draw the center 
line of ridge P which is 5" from the center line of 
rafter No. 35. See layout, Figure 73. Produce a level 
line from the intersection of the top edge of rafter 
No. 35 and the wall line, Figure 79, and measure off on 
the center line of ridge P, from this level line, the run 
of ridge P taken from the layout, Figure 73, or 10" 
as shown in Figure 79. From this point draw the pitch 
of dormer rafter No. 36. With this line as the top 
edge of the rafter draw a profile of rafter No. 36 ac¬ 
cording to the specifications and determine the plate 
level. Having developed the position of both plate 
levels independently, measure the distance between 
them, or 4 1/16", which gives the height of the dormer 
plate above the level of the main plate, Figure 79. 
The length of the rafters is determined with the steel 
square and fence in a manner similar to those of the 
main roof. 

To Lay Out Dormer T .—The rafters of dormer T 
only pitch 6" in one foot while the rafters of the main 
roof pitch 12" in one foot. The dormer is framed by 
running a header between rafter No. 21 to support the 
jack rafters of the dormer. 

To determine the height of the dormer plate draw a 
profile of common rafter No. 21, according to the 
specification, as shown in Figure 80. Project the wall 
line up indefinitely. Parallel to this line draw the cen- 


178 


COURSE IN ROOF FRAMING 


ter line of ridge 0, which is 17" from the wall line or 
19" from the facia line. See layout, Figure 73. Header 
E is located 5%" from the center of ridge 0 as shown 
on the layout, Figure 73, and on the development, Fig¬ 
ure 80. From the intersection of header R and the top 



edge of rafter No. 21 draw in the pitch of dormer 
rafter No. 22. With this line as the bottom edge of 
the rafter draw a profile of rafter No. 22 according 
to the specifications and determine the plate level. Hav¬ 
ing developed the position of both plate levels inde- 

























FRAMING AN UNEQUAL PITCH ROOF WITH DORMERS 179 

pendently, measure the distance between them, or 7", 
which gives the height of the dormer plate above the 
level of the main plate, Figure 80. The length of the 
rafters is determined with the steel square and fence 
in a manner similar to those of the main roof. 

The bevel cut of rafter No. 22 resting on rafter No. 
21 can be taken from the development, Figure 80, by 
setting a bevel to the angle as shown. This bevel can 
also be determined with the steel square. The pitch of 
the main roof is one-half pitch and referring to the 
table of pitches shown in Figure 2, a half pitch roof 
forms an angle of forty-five degrees. The pitch of the 
dormer is one-fourtli pitch and referring to the same 
table, a one-fourth pitch roof forms an angle of 26f4 
degrees. Subtracting 26V> degrees from 45 degrees will 
give the remaining angle between the two rafters, 
45 — 2614 = 181/2 degrees. Again referring to the table 
of pitches, Figure 2, 1814' degrees shows a rise of 4" 
to the foot. Use 4" on the tongue of the square and 
12" on the blade. Mark on the blade for the bevel 
cut which will give the same bevel as shown on the 
development. 

To Lay Out Dormer U .—The rafters of dormer U 
only pitch 6" in one foot while the rafters of the main 
roof pitch 12" in one foot. The dormer is framed by 
valleys G and header Q running between them, Fig¬ 
ure 73. 

To determine the height of the dormer plate draw a 
profile of jack rafter No. 46, according to the speci¬ 
fications, as shown in Figure 81. Project the wall line 
up indefinitely. Parallel to this line draw the center 


180 


COURSE IN ROOF FRAMING 


line of ridge N, which is 9" from the wall line or 11" 
from the facia line. See layout, Figure 73. 

The pitch of rafter No. 55 begins at the intersection 



of valley G, ridge N, and hip H. From this inter¬ 
section draw in the pitch of dormer rafter No. 55. With 
this line as the top edge of the rafter draw a profile of 
rafter No. 55 according to the specifications, and de- 

























































FRAMING AN UNEQUAL PITCH ROOF WITH DORMERS 181 

termine the dormer plate level. Having developed the 
position of both plate levels independently measure the 
distance between them, or 4%", which gives the height 
ot the dormer plate above the level of the main plate, 
Figure 81, upper section. The length of the rafters is 
determined with the steel square and fence in a manner 
similar to those of the main roof. 

The bevel of rafter No. 55 resting on rafter No. 57 
can be taken from the development, Figure 81, by set¬ 
ting a bevel to the angle of rafters Nos. 55 and 46, 
which gives the same bevel. This bevel can also be 
determined with the steel square. 

The pitch of the main roof is one-half pitch and 
referring to the table of pitches shown in Figure 2 a 
half pitch roof forms an angle of 45 degrees. The 
pitch of the dormer is one-fourth pitch and referring to 
the same table a one-fourth pitch roof forms an angle 
of 26% degrees. Subtracting one angle from the other 
will give the degrees of the remaining angle between the 
two rafters; 45 — 26% = 18% degrees. Again referring 
to the table of pitches, Figure 2, 18% degrees shows a 
rise of 4" to the foot. Use 4" on the tongue and 12" 
on the blade. Mark on the blade for the bevel cut, 
which will give the same bevel as shown on the develop¬ 
ment, Figure 81. 

Valley G runs from hip II to rafter No. 46. It is 
necessary to determine the exact point at which valley 
G intersects rafter No. 46. This can be developed as 
shown in the lower section of Figure 81. The top edge 
of rafter No. 55 must be in alignment with the center 
line of valley G and rafter No. 46. Project the point 



182 


COURSE IN ROOF FRAMING 


of intersection of the wall line and the top edge of 
rafter No. 55 until it intersects the top edge ot rafter 
No. 46 as shown in the top section of Figure 81. At 
right angles to this line, and from this point of inter¬ 
section on the top edge of rafter No. 46, draw a line 
parallel to the center line of ridge N until it intersects 
rafter No. 46 as in the lower section of Figure 81. 
Valley G then intersects rafter No. 46 at a point 4 y 2 " 
from the center line of ridge N and because rafter No. 
46 pitches 12" in one foot, valley G intersects rafter 
No. 46 at a point 4%" below the top edge of ridge N 
and 5/32" above the level of the main plate. 

To Lay Out Valley G. —Before setting the fence and 
square, the rise in inches per foot of run must be de¬ 
termined. The total rise is 4 y 2 " as taken from the 
development, Figure 81. The run is measured from 
rafter No. 46 to the intersection of ridge N and hip H, 
or 9 11/12", Figure 81. 

Rise in inches . . . 7 , , , 

—-———-—-—=rise m inches per toot of run . 

Run m feet 

Working this out as given in the problem we have: 

54 -r- 119/12 = 54 x 12/119 = 55/12 full = rise in 
inches. 

Set the fence and square at 5 5/12" full rise on the 
tongue and at 12" run on the blade. Mark on the tongue 
for all plumb cuts and on the blade for all level cuts. Press 
the fence firmly against the top edge of the stock and 
produce the first plumb line to the extreme right as at C, 
Figure 82. Slide the fence to the left and measure on 



183 


FRAMING AN UNEQUAL PITCH ROOF WITH DORMERS 

n lex cl line fi om plumb line 0 the run of valley G, or 
9 11/12 , and produce plumb line C, giving the extreme 
length of the valley. From the top end deduct one-half 
the thickness of hip F measured on the line of valley G 
as C-D, Figure S3, and produce plumb line D, Figure 82. 
Square this line across the top edge of the rafter and 
locate the center. 

To determine the top cut so that valley G will fit at 
the proper angle against the side of hip F, square a line 



Figure 82.—Developed Length of Valley G 


across from the point where the outside edges of the 
rafters intersect and at right angles to the center line 
until it meets the center line of valley G as at 2, Figure 
83. Then measure forward on a level line from plumb 
line D on the side of the rafter, Figure 82, the distance 
1-D, Figure 83, and produce plumb line 1, Figure 82. 
Connect plumb line 1 through the center of plumb line D 
on the top edge and produce bevel 2, top view in 
Figure 82. 













184 


COURSE IN ROOF FRAMING 



Figure 83.—Intersection of Ridge A T , Hip F and Valley G and Valley G 

Header Q 

To complete the bottom end of the valley draw in a 
section of the valley full size on the layout where the 

vallev intersects rafter No. 46 and from the extreme 

%/ 



























FRAMING AN UNEQUAL PITCH ROOF WITH DORMERS 185 



length deduct the diagonal distance of rafter No. 
46 measured on the center line of valley G as at D, 
Figure 82. The top cut is found in a manner similar 
to the top cut at upper end of the valley. Cut on plumb 
lines 1 and bevel 2 on either end of the rafter. 

To Lay Out Badge A and. Header Q .—Draw in a full 
size section of ridge N as shown in Figure 83. The run 
of the ridge is taken from the layout, Figure 73, or 9". 


Figure 84.—Front and Right Side Elevation of Problem 8, Showing 

the Method of Framing the Rafters 

From the extreme length deduct the distance C-E, Fig¬ 
ure 83. Square this line across the top edge and locate 
the center. Set a bevel square to the bevel formed by 
the intersection of ridge N and valley G. Place the 
bevel on the top edge of the ridge and draw the top 
cut through the center point. 

To Determine the Side and Top Cut of Header Q .—• 














18G 


COURSE IN ROOF FRAMING 


From the side of valley G draw a line to the pitch of 
the main roof as shown in Figure 83. Then angle L 
gives the side cut for header Q that will fit against the 
side of valley G. See top section, Figure 83. The 
header sitting at an angle forms a hopper cut and is 
developed as shown in the top section. Then L gives 
the side cut and bevel ¥ gives the top cut of header Q 



Figure 85.—Rear and Left Side Elevation of Problem 8, Showing the 

Method of Framing the Rafters 

that will fit against the side of valley G. The run is 
taken from the layout, Figure 73. 

To Assemble the Roof .—Assemble the rafters as 
shown in the elevations, Figures 84 and 85. Set up hips 
C, F, II and K and ridge 0 first. Then valley B. Then 
hips A and ridge L. Then valleys D and E and ridge M , 
supported by a pair of common rafters No. 70. Then 
valleys I and J and ridge P, supported by a pair of 
common rafters No. 36. Lastly valley G and header Q. 

















2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 


AN UNEQUAL PITCH ROOF WITH DORMERS 187 


ND LENGTHS OF RAFTERS USED 
PROBLEM NO. 8— y 2 PITCH 


IN FRAMING 


Quantity of 

Rafters 

Runs 

Lengths 

Kind of Rafters 

5 pair 

2' 0" 

2'10" 

Jack Rafters 

4 pair 

4' 0" 

5' 7Vs" 

Jack Rafters 

4 pair 

6' 0" 

8' 5%" 

Jack Rafters 

3V> pair 

8' 0" 

11' 3%" 

Jack Rafters 

1 

10' 0" 

14' 1%" 

Jack Rafter 

1 pair 

10' 0" 

14' 1%" 

Jack Rafters 

4 

10' 0" 

14' 1%" 

Common Rafters 

1 

10' 0" 

14' 1%" 

Jack Rafter 

1 

8' 0" 

11' 3 % " 

Jack Rafter 

1 pair 

6' 0" 

8' 5%" 

Jack Rafters 

1 pair 

4' 0" 

5' 77s" 

Jack Rafters 

1 pair 

2' 0" 

2'10" 

Jack Rafters 

1 

4' 0" 

5' 77s" 

Jack Rafters 

1 

6' 0" 

8' 57s" 

Jack Rafter 

1 

8' 0" 

11' 3%" 

Jack Rafter 

1 

10' 0" 

14' 1%" 

Jack Rafter 

1 

12' 0" 

16'115/ 8 " 

Jack Rafter 

1 

14' 0" 

19' 95/ s " 

Jack Rafter 

1 

16' 0" 

22' 77," 

Jack Rafter 

1 

18' 0" 

25' 514" 

Jack Rafter 

2 

19' 0" 

26'103/s" 

Jack Rafters 

9 

14' 7%" 

16' 4i/ s " 

Jack Rafters, 
Dormer “T” 

7 

5' li/ 2 " 

7' 3" 

Jack Rafters, 
Dormer “T” 

38 

2' 0" 

2'10" 

Jack Rafters 

1 

18' 0" 

25' 5V>" 

Jack Rafter 

1 

16' 0" 

22' 7i/o" 

Jack Rafter 

1 

14' 0" 

19' 95/s" 

Jack Rafter 

1 

12' 0" 

16'115/ s " 

Jack Rafter 

1 

10' 0" 

14' 1%" 

Jack Rafter 

5 

7' 0" 

9'10% " 

Cripple Rafters 

1 

5' 0" 

7' 07s" 

Cripple Rafter. 

1 

1' 0" 

1' 5" 

Cripple Rafter 

1 pair 

3' 0" 

4' 27s" 

Jack Rafters 

1 pair 

5' 0" 

7' 07s" 

Jack Rafters 

1 pair 

7' 0" 

9'10 3/4" 

Jack Rafters 

6 

6' 2i4" 

8' 9" 

Common Rafters, 
Dormer “S” 

1 pair 

4' 0" 

5' 77s" 

Jack Rafters, 
Dormer “S” 

1 pair 

2' 0" 

2'10" 

Jack Rafters, 
Dormer “S’* 

1 

2' 0" 

2'10" 

Cripple Rafter 























18S 


COURSE IN ROOF FRAMING 


RUNS AND LENGTHS OF RAFTERS USED IN FRAMING 
PROBLEM NO. 8—% PITCH—Continued 


Number of 
Rafters 

Quantity of 
Rafters 

Runs 

Lengths 

Kind of Rafters 

40 

1 

6' 0" 

8' 5%" 

Cripple Rafter 

41 

3 

r 0 " 

9'10%" 

Cripple Rafters 

42 

1 pair 

V 0" 

1' 5" 

Jack Rafters 

43 

1 pair 

3' 0" 

4' 2y s " 

Jack Rafters 

44 

1 pair 

5' 0" 

r o%" 

Jack Rafters 

45 

1 pair 

7' 0" 

9'10%" 

Jack Rafters 

46 

2 pair 

9' 0" 

12' 8%" 

Jack Rafters 

47 

1 pair 

3' 3" 

4' 7y 8 " 

Jack Rafters 

48 

1 pair 

2' 4" 

3' 3%" 

Jack Rafters 

49 

1 pair 

V 5" 

2 ' oy 8 " 

Jack Rafters 

50 

1 pair 

3' 2" 

4' 5%" 

Cripple Rafters, 
Dormer “U” 

51 

1 pair 

2' 2" 

2' 5Vs" 

Cripple Rafters, 
Dormer “U” 

52 

1 pair 

5' 2" 

7' 3%" 

Cripple Rafters, 
Dormer “U” 

53 

1 pair 

6' 5i/o" 

7' 2%" 

Cripple Rafters, 
Dormer “U” 

54 

1 pair 

7' 2" 

10' 1%" 

Cripple Rafters, 
Dormer “U” 

55 

13 

10' 0" 

11' 2Vs" 

Jack Rafters, 
Dormer “U” 

56 

1 pair 

9' 2" 

12'11%" 

Jack Rafters, 
Dormer “U” 

57 

9 

10' 2" 

11' 2Vs" 

Jack Rafters, 
Dormer “U” 

58 

1 

2' 0" 

2'10" 

Cripple Rafter 

59 

1 

6' 0" 

8' 57s" 

Cripple Rafter 

60 

1 

10' 0" 

14' 1%" 

Cripple Rafter 

61 

1 

14' 0" 

19' 9%" 

Cripple Rafter 

62 

1 

16' 0" 

22' 77." 

Cripple Rafter 

63 

1 

12' 0" 

16'11%" 

Cripple Rafter 

64 

1 

8' 0" 

11' 3%" 

Cripple Rafter 

65 

1 

4' 0" 

5' 77s" 

Cripple Rafter 

66 

1 

2' 0" 

2'10" 

Cripple Rafter 

67 

2 

4' 0" 

5' 77s" 

Cripple Rafters 

68 

1 pair 

1' 0" 

1' 5" 

Jack Rafters, 
Dormer “W” 

69 

1 pair 

3' 0" 

4' 27s" 

Jack Rafters, 
Dormer “W” 

70 

4 

4' 21,4" 

5'11" 

Common Rafters, 
Dormer “W” 

71 

1 pair 

6' 0" 

8' 57s" 

Jack Rafters 

72 

1 pair 

4' 0" 

5' 77s" 

Jack Rafters 
































FRAMING AN UNEQUAL PITCH ROOF WITH DORMERS 189 


RUNS AND LENGTHS OF RAFTERS USED IN FRAMING 
PROBLEM NO. 8—% PITCH—Continued 


Number of 
Rafters 

Quantity of 
Rafters 

Runs 

Lengths 

Kind of Rafters 

A 

1 pair 

14' 1%" 

17' 3 % " 

Hip Rafters 

B 

1 

14' 1%" 

17' 3%" 

Valley Rafter 

C 

1 

24' 0%" 

29' 5%" 

Part Hip and 

Part Valley 

D 

1 

12' 8%" 

15' 7" 

Valley Rafter 

E 

1 

9'10%" 

12' 114" 

Valley Rafter 

F 

1 

26'10%" 

32'10%" 

Hip Rafter 

G 

1 pair 

9'11" 

lO'lO" 

Valley Rafter 

H 

1 

26'10%" 

32'107s" 

Hip Rafter 

I 

1 

14' 1%" 

17' 3%" 

Valley Rafter 

J 

1 

19' li/s" 

23' 4%" 

Valley Rafter 

K 

1 

26'10%" 

32'10%" 

Hip Rafter 

L 

1 

14' 0" 

14' 0" 

Ridge 

M 

1 

7' 0" 

7' 0" 

Ridge 

N 

2 

9' 0" 

9' 0" 

Ridge 

0 

1 

18' 0" 

18' 0" 

Ridge 

P 

1 

10' 0" 

10' 0" 

Ridge 

Q 

1 

32' 0" 

32' 0" 

Header 

R 

1 

16' 0" 

16' 0" 

Header 


Figures used on the steel square: 

Main roof and dormers 8 and T, 12" on tongue, 12" 
on blade. Mark on tongue for all plumb cuts and on 
blade for all level cuts. 

Top cut for jack and cripple rafters, main roof and 
dormers S and T, 12" on tongue, 17" on blade. Mark 
on blade for top cut. 

Dormers T and U, 6" on tongue, 12" on blade. Mark 
on tongue for all plumb cuts and on blade for all level 
cuts. Take top cuts from the layout. 

Hip and valley rafters, excepting valleys G, 12" on 
tongue, 17" on blade. Mark on tongue for all plumb 
cuts and on blade for all level cuts. 

Top cut for hip and valley rafters, excepting valley G, 


























190 


COURSE IN ROOF FRAMING 


8%" on tongue, 10%" on blade. Mark on blade for top 
cut. 

5 " 

Valley G, 5—. on tongue, 12" on blade. Mark on tongue 

for all plumb cuts and on blade for all level cuts. Pick 
up top cuts from the layout. 



CHAPTER VII 

HOW TO FRAME A GAMBREL ROOF 

A gambrel roof is a roof the slope or pitch of which 
is broken. That is, instead ot the gable end having one 
continuous slope or pitch it is composed of two slopes 
01 pitches, the lower half of the roof having the greater 
pitch. See Figure 87. 

The method ot framing the rafters is similar to that 
for any other equal pitch roof. The walls of the build¬ 
ing form the lower plate upon which the steeper rafters 
lest. A second plate is stationed at the proper height 
to receive the upper rafters, being securely tied across 
the building to keep it from spreading under the 
weight. The upper and lower rafters are framed in¬ 
dependently, the upper rafters to the lesser pitch and 
the lover rafters to the steeper pitch, the effect being 
that of one roof placed upon another. 

The proper proportions to use in laying out a 
gambrel roof is a matter depending upon individual 
judgment and the needs and desires of the owner and 
architect. Some builders give the upper rafters a 
very flat pitch, while others give a very steep pitch. 
In this problem the knuckle joint is placed half way 
between the facia line and the ridge, thus making both 
sets of rafters of the same length. 

Specifications .—Lower plate, %" x 2 y 2 ". 

Upper plate, %" x 

Valley rafters, %" x I 14 ". 

191 


192 


COURSE IN ROOF FRAMING 



Figure 86.—Plan of Gambrel Roof, from Which the Working Layout 

Is Made 











































































HOW TO FRAME A GAMBREL ROOF 


193 


Common and jack rafters, s/ 8 " x 

Ridge, %" x li/ s ". 

Projection, 1V 2 ". 

Facia, 

Plancher level to plate level, lower 
rafters, 2y 4 ". 

Pitch (see development, Figure 87). 

Dimensions (see plan, Figure 86). 

Rafters spaced 2" on centers. 

Layout.- A full size working 1 layout of the plan, 
Figure 86, should be drawn on a board or a sheet of 
detail paper. The layout will represent a scale of 1" 
to the foot. In applying the various measurements full 
size, substitute the word feet for inches in listing the 
runs and lengths of the rafters. Number each rafter 
and ridge as shown on the plan. Put the corresponding 
numbers on the rafters as they are laid out to insure 
their ready identification and proper location during the 
erection of the roof. 

It will also be necessary to develop an end view of 
the gable as shown in Figure 87 to determine the 
pitch or slope of the upper and lower rafters and also 
the. heights of the plate levels. A graphic method for 
laying out the slope of the rafters is shown in Figure 
88 . The low ei i afters form an angle of sixty degrees 
with the plate level and the upper rafters thirty degrees 
with the plate level, making both sets of rafters of 
the same length. Lay in a center and a base line at 
right angles to each other and of indefinite length. 
Bisect the angle as follows: With U as a center and 
any convenient radius, scribe an arc cutting the base 


194 


HOW TO FRAME A GAMBREL ROOF 


line as at 1. With U as a center and the same radius, 
s-cribe an arc cutting the center line as at 2. With 1 
and 2 as centers and the same radius, scribe the arc as 
at 3. From U, through arc 3, draw a line of indefinite 
length, bisecting the right angle. 



Figure 87.—End View. Showing' Method of Developing Profiles of the 
Common Rafters. With the Pitch, Projection, Width of Facia and 
Plancher Level Known, the Plate Level Can Be Determined 

t 

Measure off on the base line from the center line U 
a distance equal to the total run of the common rafters 
from the center of the ridge to the facia line, this being 
one-lialf the span of the building plus 1 projection, 
1114", as at A, Figure 88. From point A draw in 


















































195 


HOW TO FRAME A GAMBREL ROOF 


the top edge of the lower rafters at an angle of sixty 
degrees. i he three sides of an equilateral triangle 
being- equal form angles of sixty degrees. To form the 
side of the triangle from the point A, use A as a center 



Figure 


88.—Graphic Method for Laying Out the Pitch of the Common 
Rafters at 30 and 60 Degree Angles 


and with any convenient radius scribe an arc cutting 1 
the base line as at 4. With 4 as a center and the same 
radius scribe part of a circle. With A as a center and 
the same radius arc the circle as at 5. From the point A 




















196 


COURSE IN ROOF FRAMING 


on the base line draw a line through arc 5 until it 
intersects the center line as at Y. This gives the slope 
of the lower rafters at an angle of sixty degrees. 

The slope of the rafters can also be laid out with 
the steel square by using 16%" on the blade and 9%" 
on the tongue, adjusting the square so that these figures 
lie accurately on the base line and marking on the blade 
for the slope of the lower rafters. Measure off on the 
center line from the base line at U a distance equal 
to the total height of the roof, 11as at T. From 
the point T draw in the top edge of the upper rafters 
at an angle of thirty degrees. A simple way to de¬ 
termine this pitch is to lay in another equilateral tri¬ 
angle. Since a quarter circle contains ninety degrees, 
the triangle, sixty degrees, deducted from the ninety 
degrees will leave an angle of thirty degrees. From 
point Y draw a plumb line as at X. With Y as a 
center and any convenient radius scribe part of a circle. 
With A as a center and the same radius, arc the circle 
as at 6. From the point Y through arc 6 draw a line 
intersecting the center line, which should meet exactly 
at the point T. The slope of the rafters can also be 
laid out with the steel square by drawing a level line 
through the point Y and using 1.6%" on the blade and 
9%" on the tongue, adjusting the square so that these 
figures lie accurately on the level line and marking on 
the tongue for the slope of the upper rafters at an 
angle of thirty degrees with the plate level. 

With the top edge or outside lines of the roof de¬ 
termined, lay in a profile of both lower and upper 
rafters as shown in Figure 87, according to the dimen- 


HOW TO FRAME A GAMBREL ROOF 


197 


sions given in the specifications, so that the plate levels 
can be determined. In this problem the knuckle joint 
is midway between the facia line and the ridge. The 
edge of the upper plate forms the joint, making both 
sets of rafters the same length, locating the upper 
plate 5%" above the lower plate and the main plate 
level 214 " above the planclier level. 

To Lay Out Lower Common Rafters .—Before setting 
the square, the rise in inches per foot must be de¬ 
termined. The run, 12", a constant unit, remains un¬ 
changed. The run of rafter No. 5, measured on the 
layout Figure 86, measuring from the upper plate line 
to the facia, is dpi". See development, Figure 87. The 
total height from the top of the facia line A to the 
top of the upper plate level, Figure 87, Y, is 7^4". 
Thus, with the total rise 7%" and the total run 4*4", find 
the rise in inches per foot. 

Rise in inches . . . 7 , 

.- : — : -= rise m inches per foot. 

Run in feet 

71/ 22 

-~L±x~=--=20y 2 "== rise in inches per foot. 

/ 

Set the fence and square at rise on the blade 

and 12" run on the tongue. Mark on the blade for all 
plumb cuts and on the tongue for all level cuts. Press 
the fence firmly against the top edge of the stock to be 
used for the common rafter and produce the facia line 
or the first plumb line to the extreme left, A, Figure 89. 
Slide the square to the right and measure on a level line 
from the facia line the run of the rafter, 4%", and 





198 


COURSE IN ROOF FRAMING 



End View 

Figure 89.—Developed Length 


of Lower Common Rafter No. 5 


L|lu 

































HOW TO FRAME A GAMBREL ROOF 


199 


pi ounce the plumb cut against the upper plate, giving 
tne extreme length of the lower common rafters. No 
deduction is to be made from this length but the end 
of the rafters should be notched out to receive the 
uPPer plote, forming a strong and rigid brace. Meas¬ 
ure down on plumb line Y from the top edge of the 
rafter the thickness of the upper plate, and pro¬ 
duce a level line on which the bottom of the plate will 
rest, as at S, Figure 89. Measure in from facia line A 
1 %", tlle width of the projection, and produce wall 
line h. Measure down on the facia line from the top 
edge of the 1 after % the width of the facia, and pro¬ 
duce plancher level F. Measure up from plancher level 
F, on a plumb line, 2locating plate level G. Cut 
on line A for the facia, on line F for the plancher level, 
on lines G and B for the birdsmouth and on plumb 
line 1 and level line S for the notch against the upper 
plate. 

To Lay Out Lower Jack Rafters .—The lengths of 
jack rafters Nos. 6, 7 and 8 are determined jn the 
same manner as the preceding common rafter No. 5 
since they are a part of the length of it. Take the runs 
from the layout, Figure 86, measuring from the center 
of the valley to the upper plate or inner wall line. The 
three rafters are shown developed on the side of a 
single rafter, Figure 90. In practice these would be 
laid out separately but are here laid out over one an¬ 
other to save space and to avoid repetition. Press the 
fence firmly against the top edge of the rafter, using 
the same figures on the square as before, and produce 
the first plumb line to the extreme right, A, Figure 90. 


200 


COURSE IN ROOF FRAMING 



End View 


Figure 90.—Developed Length of Lower Jack Rafters Nos. 6 


7 and 8 


k 









































HOW TO FRAME A GAMBREL ROOF 


201 


„ U ‘ S 1 ' c squ f re to tlle left and measure on a level line 
rom plumb line F the run of rafter No. 6, 4V," the run 

of rafter No. 7, 2%" ■, and the run of rafter No. 8, 3 /,". 
aiu produce plumb line C the extreme length of the lower 
jack rafters. No deductions are to be made from these 
engths but the end of the rafters should be notched 
out to receive the upper plate, forming a strong and 
rigid brace. Measure down on plumb line Y from the 
,°P 0° rafter the thickness of the upper plate, 

M , and produce a level line on which the bottom of 
the plate will rest as at S, Figure 90. The lower ends 
oi the rafters are beveled to make a tit against the side 
of the valley rafter. From the extreme length obtained 
with the fence and square, which is to the center line 
of the valley, must be deducted one-half the thickness 
of the valley measured on the line of the jack rafters, 
or one-half the diagonal thickness of the valley, which 
is y 2 " full. Measure back on a level line from C, Figure 
90,^ on the side of the rafter, this diagonal thickness, 
L" full, and produce another plumb line as at D. 
Square this line across the top edge of the rafter and 
locate the center. 


To lay out the top cuts so that the jack rafters will 
fit against the side of the valley rafter at the proper 
angle measure forward on a level line from plumb line 
I) a distance equal to one-half the thickness of the 
stock used for the jack rafter, or 3/16" (the thickness 
of stock specified being %") and produce plumb line 1. 
Connect, plumb line 1 through plumb line D on the 
center line as shown at 2, top view, Figure 90. This 
top cut can also be laid out with the steel square by 


202 


COURSE IN ROOF FRAMING 


using the length, 23%" (bridge measure of the run, 12", 
and the rise, 20y 2 ") on the blade and the run, 12", on 
the tongue. Mark on the blade for the top cut. 

Rafter No. 7 rests on the lower plate which must 
be cut for the birdsmouth similarly to the common 
rafters. This can readily be laid out by using a com¬ 
mon rafter for a pattern or laying out as before. 
Measure in from facia line A lbo", the width of the 
projection, and produce wall line B. Measure down on 
facia line A from the top edge of the rafter the 
width of the facia, and produce plancher level F. 
Measure up from the plancher level, on a plumb line, 
21/4", locating plate level G. 

For rafter No. 6 cut on plumb line 1 and on bevel 2 
for the cheek and side cut against the valley and on 
line F for the plancher level. For rafter No. 7 cut on 
plumb line 1 and on bevel 2 for the cheek and side cut 
against the valley and on line G for the plate level. 
For rafter No. 8 cut on plumb line 1 and on bevel 2 for 
the cheek and side cut against the valley. On all three 
rafters, Nos. 6, 7 and 8, cut on the plumb line Y and 

level line S for the notch against the upper plate. Cut 

1 pair of jacks No. 6 and 2 pair of each Nos. 7 and 8. 

To Lay Out Lower Valley Rafters .—Valley rafters 
of an equal pitch roof cross the plate at an angle of 
forty-five degrees or the diagonal of a square; there¬ 
fore, the unit to use in laying out the valley is the 

diagonal of 12" and 12" or 17", this being the constant 
unit used in laying out hip and valley rafters. The 
rise remains the same as for the common rafters, 
2014". Set the fence and square at 20y 2 " rise 011 the 


HOW TO FRAME A GAMBREL ROOF 


203 


blade and 17" run on the tongue, or for convenience 
these figures can he divided by two, giving 1014” rise 
on the blade and 8%" rise on the tongue. Mark on 
the blade for all plumb cuts and on the tongue for all 
level cuts. Take the run from the layout, Figure 86, 
measuring on the center line of the valley from the 
facia line to where it intersects the corner of the 


3 / 

inner wall line, or 6-^". Press the fence firmly against 

the top edge of the stock to be used for the valley and 
produce the facia line or the first plumb line to the 
extreme left, A, Figure 91. Slide the square to the 
right and measure in on a level line from the facia 


3/ 

line, the run of the valley, 6y^", and produce the plumb 

cut against the upper plate, giving the extreme length 
of the lower valley rafter. No deductions are to be 
made from this length but the corners must be beveled 
to fit into the corner formed by the intersection of the 
return and main plates. 


To lay out the top cuts so that the valley will fit 
into the corner, square line Y across the top edge of 
the rafter and locate the center point. From plumb line 
Y measure forward on a level line a distance equal to 
one-lialf the thickness of the stock used for the valley, 
or %" (the thickness of stock specified being %") and 
produce plumb line 5. Square this line across the top 
edge of the rafter and connect the outside points with 
the center as shown at 6, top view, Figure 91. This 
top cut can also be laid out with the steel square by 
using 1314" (one-half the bridge measure of the run 



204 


COURSE IN ROOF FRAMING 


17" and the rise 20%") on the blade, and 8%" (one- 
half the unit for the run 17") on the tongue. Mark on 
the blade for the top cut. 



To complete the lay-out of the lower end of the rafter 
square facia line A across the top edge of the rafter and 
locate the center point. 




















HOW TO FRAME A GAMBREL ROOF 


205 


To lay out the bevel on the facia line, measure back 
on a level line from facia line A a distance equal to 
one-half the thickness of the stock used, and pro¬ 
duce plumb line 3, Figure 91, on the side of the rafter. 
Connect plumb line 3 through the center point on the 
top edge as shown in the top view. This top cut is the 
same cut as that previously described for laying out 
the top end. 

The valley crosses the projection at an angle of forty- 
five degrees; therefore, the distance to be measured in 
locating the wall line is the diagonal of l 1 /^" and 1%", 

the width of the projection, or 2^~". 

±~i 


To lav out the birdsmouth measure in on a level line 
«/ 

from facia line A, 2—--", the diagonal of the projection, 

1 Aj 


and produce wall line B . Measure down on facia line A 
from the top edge of the rafter, the width of the 
facia, and produce plancher level F Measure up from 
plancher F, on a plumb line, 2f4 ,r > locating plate level G. 

To make a fit against the side of the plate square 
wall line B across the bottom edge of the rafter and 
locate the center point. Measure back on a level line 
from plumb line B, on the side of the valley, a distance 
equal to one-half the thickness of the stock used for the 
valley, or and produce plumb line 1. Square this 
line across the bottom edge and connect through the 
center point as shown at 2 on the bottom view, Figure 
91. Cut on plumb line 3 and on bevel 4 for the facia, 
on line F for the plancher level. On line G make a 
square cut. On plumb line 4 and on bevel 2 cut for the 



206 


COURSE IN ROOF FRAMING 


birdsmouth and on bevels 6 on plumb line 5 for the tit 
against the walls. Cut two valleys the same length 
in pairs. 

To Lay Out Upper Common Rafters. —Before setting 
the square the rise in inches per foot must be de¬ 
termined. The run 12", a constant unit, remains un¬ 
changed. The run of common rafter No. 1, measured 
on the layout, Figure 86, measuring from the inner plate 
or upper wall line to the center of the ridge, is 7*4". 
See development, Figure 87. The total height from the 
top of the plate to the top of the ridge is 414 ". Thus, 
with a total rise of 4f4" and a total run of 7 1 / 4", find the 
rise in inches per foot. 


Rise in inches 
Run in feet 


P 1 ¥ = 7” 
7% 1 


— rise in inches per foot. 
~ rise in inches per foot. 


Set the fence and square at 7" rise on the tongue 
and 12" run on the blade. Mark on the tongue for all 
plumb cuts and on the blade for all level cuts. Press 
the fence firmly against the top edge of the stock to be 
used for the valley rafter and produce the wall line 
or first plumb line to the extreme left, A, Figure 92. 
Slide the square to the right, and measure on a level 
line from the wall line A the run of the valley, 7 1 / 4", 
and produce line T, the extreme length to the center 
of the ridge. From this length deduct one-half the 
thickness of the ridge, 3/16" (the thickness of stock 




HOW TO FRAME A GAMBREL ROOF 


207 


specified being %"), and produce plumb line D, Figure 
92, the cutting length of the rafter against the ridge. 

To form the notch over the upper plate measure in 
on a level line from plumb line A the width of the 
upper plate, and produce plumb line B. From 

where plumb line A intersects the top edge of the 



valley produce a level line until it meets plumb line B, 
as at G. Cut on lines G and B for the notch over the 
upper plate and on line I) for the cut against the ridge. 

To Lay Out Upper Jack Buffers .—The lengths of jack 
rafters Nos. 2, 3 and 4 are determined in the same 
manner as for the preceding common rafter No. 1, since 
they are a part of the length of it. Take the runs 
from the layout, Figure 86, measuring from the center 
of the valley rafter to the center of the ridge. The 




















208 


■COURSE IN ROOF FRAMING 


three rafters are shown developed on the side of a 
single rafter, Figure 93. In practice these would be 
laid out separately but are here laid out over one 
another to save space and to avoid repetition. Press 
the fence firmly against the top edge of the rafter 
stock, using the same figures on the square as before, 
and produce the first plumb line to the extreme right, T, 



Figure 93, working from the ridge end of the rafter 
instead of from the facia line. Slide the square to 
the left and measure on a level line from the ridge 
line T the run of rafter No. 2, b"; the run of rafter No. 
3, 4"; and the run of rafter No. 4, 2"; and produce 
plumb line C, giving the extreme length of the upper 
jack rafters. From the ridge end of the rafter measure 
forward on a level line one-half the thickness of the 



































HOW TO FRAME A GAMBREL ROOF 2 09 

ridge, 3/16", from plumb line T and produce plumb line 
D, the cutting length of the jacks. 

The lower ends of the rafters are beveled to make a 
fit against the side of the valley rafter. From the 
extreme length obtained with the fence and square, 
which is to the center line of the valley rafter, must be 
deducted one half the thickness of the valley measured 
on the line of the jack rafters, or one-half the diagonal 
thickness of the valley, which is full. Measure 
back on a level line from plumb line C, Figure 93, this 
diagonal thickness, full? and produce another plumb 
line as at D. Square this line across the top edge of 
the rafter and locate the center. 

To lay out the top cut so that the jack rafters will 
fit against the side of the valley rafter at the proper 
angle measure forward on a level line from plumb line 
D a distance equal to one-half the thickness of the stock 
used for the jack rafter, 3/16", and produce plumb line 
1. Connect plumb line 1 through plumb line D on the 
center line as shown at 2, top view, Figure 93. This 
top cut can also be laid out with the steel square by 
using the length, 13%" (bridge measure of the run, 
12", and the rise, 7") on the blade and the run, 12", 
on the tongue.' Mark on the blade for the top cut. Cut 
on plumb line 1, and on bevel 2 for the cheek and side 
cut against the valley and on line D for the cut against 
the ridge. 

To Lay Out the Upper Valley Rafter .—The rise of 
the valley, 7", remains the same as for the common 
and jack rafters. The constant unit for the run changes 



210 


COURSE IN ROOF FRAMING 


to 17", the diagonal of 12" and 12". Set the fence and 
square at 7" rise on the tongue and 17" run on the 
blade. Mark on the tongue for all plumb cuts and on 
the blade for all level cuts. Take the run from the lay¬ 
out, Figure 86, measuring on the center line of the 
valley rafter from the upper wall line to the ridge, or 
10V 4 ". Press the fence firmly against the top edge of 
the stock to be used for the valley and produce plumb 
line A at the extreme left, Figure 94. Slide the square 



to the right and measure in on a level line from plumb 
line A the run of the valley, 1014", and produce plumb 
line T, giving the extreme length of the upper valley 
to the center of the ridge. It will be better construction 
to butt ridge D against ridge C and fit the valleys into 
the corner formed by the intersection of the two ridges. 

To determine the cutting length of the valley deduct 
from the upper end of the rafter one-lialf the thickness 
of the ridge measured on the line of the vallev or one- 
















HOW TO FRAME A GAMBREL ROOF 


211 


half the diagonal thickness of the ridge, 14 ". Measure 
forward on a level line from plumb line T, Figure 94, 
and produce plumb line D. Square line D across 
the top edge of the rafter and locate the center point. 

To lay out the top cut so that the valley will fit 
into the angle formed by the intersection of the two 
rid ges, measure forward on a level line a distance equal 
to one-half the thickness of the stock used for the 
valley, %", and produce plumb line 1. Square this 
line across the top edge of the rafter and connect the 
outside points with the center as shown at 2 , top view, 
Figure 94. This top cut can also be laid out with the 
steel square by using 9%" (one-half the bridge measure 
of the run 17" and the rise 7") on the blade and 8 1 //' 
on the tongue. Mark on the blade for the top cut. 

To complete the layout of the lower end of the valley 
produce a level line G from the intersection of the top 
edge of the rafter and plumb line A, locating the plate 
level. Cut on line G for the plate level, and on plumb 
line 1 and top cut 2 for the ridge cut. 

To Lay Out the Ridges .—The run of the ridges is 
taken from the layout, Figure 86. For ridge C measure 
the extreme length of the roof from wall to wall, or 
2'8". For ridge D measure from the center of ridge C 
to the facia line, or lib*". From this length deduct 
one-half the thickness of ridge C, or 3/16", making the 
net length of ridge D 11 5/16". 

To Assemble the Roof .—Assemble the rafters as 
shown in the elevation, Figure 95. Set up ridges C and 
D first, securing them in place with the common rafters. 
Fasten the valleys next, keeping the center lines in 



212 


COURSE IN ROOF FRAMING 


alinement from the facia line to the ridges. Fasten 
the jack rafters last. 

Runs and Lengths of Rafters .—The following table 
is prepared to assist the student in checking up his 
work. It is intended that the framer will take his runs 



Figure 95.—Elevation of Gambrel Roof, Showing Method of Framing 

Rafters 

from the layout nad develop the lengths with the steel 
square and fence, using the table only as a matter of 
information, giving him the assurance that he has 
taken the proper run and determined the correct length 
of the rafters. The measurements listed in the table 
are extreme lengths on the center lines. Make allow- 









HOW TO FRAME A GAMBREL ROOF 


213 


ances where rafters intersect a ridge or valley rafter 
for the cutting lengths. It is suggested that the reader 
frame a model ot the roof for practice, building it on 
the same scale as the layout, 1" to the foot. In using 
the table read feet as inches; for example, on rafter 1, 


the run would read 



// 


and the length 8 


12 * 


The 


square being laid out in twelfths of an inch, it is an 
easy matter to check up the work accurately. 


RUNS AND LENGTHS OF RAFTERS USED IN FRAMING 

GAMBREL ROOF 


Number of 
Rafters 

Quantity of 
Rafters 

Runs 

Lengths 

Kind of Rafters 

1 

33 

7' 3" 

8' 4%" 

Upper Common 
Rafters 

> 

L* 

2 pair 

6' 0" 

6'11%" 

Upper Jack 

Rafters 

3 

2 pair 

4> 0" 

4' 7%" 

Upper Jack 

Rafters 

4 

2 pair 

2' 0" 

2' 3%" 

Upper Jack 

Rafters 

5 

23 

4' 3" 

8' 5" 

Lower Common 
Rafters 

6 

1 pair 

4' 3" 

8' 5" 

Lower Jack 

Rafters 

7 

2 pair 

2' 9" 

5' 5 % " 

Lower Jack 

Rafters 

8 

2 pair 

O' 9" 

1' 5%" 

Lower Jack 

Rafters 

A 

1 pair 

10' 3" 

11' iy s " 

Upper Valley 
Rafter 

B 

1 pair 

6' 0%" 

9' 5Vs" 

Lower Valley 
Rafter 

C 

1 

32' 0" 

32'' 0" 

Ridge 

D 

1 

11' 6" 

11' 6" 

Ridge 


Figures to use on the steel square: 

Upper common and jack rafters, 7" on tongue, 12" 



















214 


COURSE IN ROOF FRAMING 


on blade. Mark on tongue for all plumb cuts and on 
blade for all level cuts. 

Top cut for upper jack rafters, 12" on tongue, 13%" 
on blade. Mark on blade for top cut. 

Upper valley rafters, 7" on tongue, 17" on blade. 
Mark on tongue for all plumb cuts and on blade for 
all level cuts. 

Top cut for upper valley rafters, 8%" on tongue, 
9%" on blade. Mark on blade for top cut. 

Lower common and jack rafters, lO 1 ^" on tongue, 
6" on blade. Mark on tongue for all plumb cuts and 
on blade for all level cuts. 

Top cut for lower jack rafters, 12" on tongue, 23%" 
on blade. Mark on blade for top cut. 

Lower valley rafters, 101/4" on tongue, 8%" on blade. 
Mark on tongue for all plumb cuts and on blade for 
all level cuts. 

Top cut for lower valley rafters, 8%" on tongue, 
13 i/ 4 " on blade. Mark on blade for top cut. 


CHAPTER VIII 

HOW TO DETERMINE THE LENGTHS OF ROOF RAFTERS 

A useful accessory to the equipment of roof framers 
for determining the length of rafters of various pitches 
is shown in Figures 96, 97 and 98. The diagrams should 
be laid off on well seasoned stock, preferably three-ply 
material, or better still made of metal and machined. 
The distances must be measured off accurately as the 
least variation will be greatly magnified in picking up 
a required length and the rafter will be either too 
short or too long. 

To make a diagram for listing the lengths of common, 
jack and cripple rafters, draw a base line as in Figure 
96 and at right angles to the base line draw a perpen¬ 
dicular line of indefinite length. Mark off on the base 
line from the intersection of the perpendicular line 
twelve one-inch spaces, the unit of one foot of run of 
the common rafter. Mark off on the perpendicular line 
from the intersection of the base line twelve one-inch 
spaces, giving various pitches from nothing up to one- 
lialf pitch. From zero on the base line number the 
spaces consecutively from 1 to 12 and subdivide each 
inch into one-eiglith inch spaces. From the base line 
on the perpendicular line number the spaces consecu¬ 
tively from 1 to 12. Connect the spaces marked off on the 
perpendicular line with zero. Project all spaces marked 
off on the base line upward until they intersect the last 
pitch line. All lines should be laid in with a sharp knife. 

215 


216 


COURSE IN ROOF FRAMING 


To illustrate the use of the diagram, suppose the 
span of a building is 20'0" with % pitch. The run 
of the common rafter would be lO'O" or one-half the 
span of the building, the rafters rising 9" in one foot 



Figure 96.—Diagram for Obtaining Lengths of Common, Jack and 

Cripple Rafters 

of run. Lay a rule on the 9" pitch line on the diagram 
and follow the 10" mark on the base line upward until 
it intersects the 9" pitch line, as at A, Figure 96, then 
the distance on the pitch line from zero to A is the 
length of the rafter, or 12% feet. In a similar manner 





















































































































































HOW TO DETERMINE LENGTHS OF ROOF RAFTERS 217 

for rafters from 1" to 12" rise per foot and runs from 
l'O" to 12'0" tlie lengths may be readily determined. 
In reading the measurements on a standard rule when 
picking up the lengths read inches as feet. Any pitch 
can be determined in a similar manner by subdividing 
the divisions on the perpendicular line and connecting 
the points with zero on the base line, making the use 
of the diagram very flexible. 

To make a diagram for listing the lengths of hip 
and valley rafters draw a base line as in Figure 97 
and at right angles to the base line draw a perpen¬ 
dicular line of indefinite length. Mark off on the base 
line from the intersection of the perpendicular line 
seventeen one-inch spaces, the unit of one foot run 
of the hip and valley rafter. Mark off on the perpen¬ 
dicular line from the intersection of the base line twelve 
one-inch spaces, giving the various pitches from noth¬ 
ing to one-half pitch. From zero on the base 
line number the spaces consecutively from 1 to 17 
and subdivide each into one-eighth inch spaces. 
From the base line on the perpendicular line number 
the spaces consecutively from 1 to 12. Connect the 
spaces marked off on the perpendicular line with zero. 
Project all spaces marked off on the base line upward 
until they intersect the last pitch line. Lay off all 
lines with a sharp knife. 

To illustrate the use of the diagram, suppose the 
span of the building, as in the previous illustration, 
is 20'0" with % pitch. The run of the common rafter 
would be lO'O", or one-half the span, and the run of 
the hip rafter would be the diagonal of lO'O" and lO'O" 


218 


COURSE IN ROOF FRAMING 


or 14'1%", which is found by laying the rule on the 
diagram, Figure 96, and measuring the distance from 
zero to 10" rise, the diagonal of 10 and 10, as at B, 



Figure 96. Having found the run of the hip rafter, lay 
the rule on the diagram, Figure 97, on the 9" pitch 
line and follow the 14%" full mark (1%" is approxi- 














































































































































































HOW TO DETERMINE LENGTHS OF ROOF RAFTERS 219 


mately % of a foot) on the base line upward until it 
intersects the 9" pitch line as at A, Figmre 97. Then 
the distance on the pitch line from zero to A is the 
length of the hip rafter, lGT 1 /?". In reading the meas¬ 
urements on a standard rule in picking up the lengths 
read inches as feet. Any pitch can he determined in 
a similar manner by subdividing* the divisions and con- 
necting the points with zero on the base line, making a 
very flexible diagram and a useful accessory. 

Still another method for determining the lengths of 
hip and valley rafters is shown in Figure 98. Draw 
a base line as in Figures 96 and 97 and at right angles 
to the base line draw a perpendicular line of indefinite 
length. Mark oil on the base line from the intersection 
of the perpendicular line, 17", the unit of one foot run 
of the hip and valley rafters. Mark off on the perpen¬ 
dicular line from the intersection of the base line 
twelve one-incli spaces, giving the various pitches from 
nothing to one-lialf pitch. Divide the distance 
from zero on the base line to the intersection 
of the base line and perpendicular line into twelve 
equal parts and divide each twelfth division into eighths. 
From zero on the base line number each one-twelfth 
division consecutively from 1 to 12. From the base 
line on the perpendicular line number each space con¬ 
secutively from 1 to 12. Connect each division on the 
perpendicular line with zero. Project all spaces marked 
off on the base line upward until they intersect the last 
pitch line. Lay in all lines with a sharp knife. 

To illustrate the use of the diagram, suppose the span 
of the building, as in the previous illustrations, is 20'0" 


One foot Run- hip and Valley Raftere 


220 


COURSE IN ROOF FRAMING 



















































































































HOW TO DETERMINE LENGTHS OF ROOF RAFTERS 221 


with % pitch. The run of the common rafter would he 
10'0", or one-half the span. Lay a rule on the 9" pitch 
line on the diagram and follow the 10" mark on the 
base line upward until it intersects the 9" pitch line, 
as at A, Figure 98. Then the distance on the pitch 
line from zero to A is the length of the hip or valley 
rafter, or 16 'iy 2 ", giving the same result as in the 
diagram, Figure 97. 


CHAPTER IX 


HOW TO FRAME A CURVED RAFTER ROOF 

A curved rafter roof is a moulded or curved roof 
such as an “ogee” roof over a bay window, an eye¬ 
brow window opening, a curved tower roof, a gothic 
roof, a circular dome, etc. The profile of a section 
of the roof surface determines the profile or curve to 
which the top edge of the common rafters are shaped. 

The curve of the hip rafter is entirely different and 
must he developed from the curve of the common rafter 
in order to bring the center line of the hip in alignment 
with the top edge of the common and jack rafters. 

The run of the hip rafter is longer than the run of 
the common rafter, but the total rise of both rafters is 
the same because they terminate at the apex, or, in 
other words, the profile of the hip rafter is an elon¬ 
gated profile of the common rafter. 

This introduces an important problem in the de¬ 
velopment of curved surfaces and offers an excellent 
study in picking up lines and bevels from the plan 
where the hips do not cross the plates at an angle of 
forty-five degrees. 

Specifications .—Plate, %" x 2". 

Hip rafters, %" x 3". 

Jack rafters, %" x 3". 

Total rise, 15". 

Dimensions (see plan). Figure 99. 

Rafters spaced 2" on centers. 

222 


HOW TO FRAME A CURVED RAFTER ROOF 


223 



Figure 99.—Plan of Curved Rafter Roof, from Which the Working 

Layout Is Made 






































224 


COURSE IN ROOF FRAMING 


Layout .—A full size working layout of the plan, 
Figure 99, should be drawn on a board or a sheet of 
detail paper. To ajjply the measurements taken from 
the layout, which represents a scale of 1" to the foot, 
substitute the word feet for inches in listing the lengths 
of the rafters. 

A simple way to lay out the hexagonal plate is shown 
in Figure 99. The length of a side of a true hexagon 
is equal to the radius of a circumscribed circle. Draw 
a horizontal line and mark the center as at G. With G 
as a center and a radius of 10". the required length of 
a side of the hexagonal plate, scribe a circle. Use the 
point where the center line arcs the circle for a center, 
as at J, and with a pair of dividers or trammel points 
set to the radius of the circle, arc the circle on either 
side of the center line as at E, Figure 99. Connect J 
and E, giving the sides of the hexagon. Connect G-E 
on the points of the hexagon, giving the center lines of 
the hip rafters. Divide each side of the hexagon into 
five equal spaces and draw in the center lines of the 
jack rafters spaced 2" apart. The hexagonal plate can 
also be laid out with the steel square by using 9%" 
on the tongue and 16%" on the blade. Place these two 
figures so they coincide with the center line. Mark 
along the tongue for the angle of the hexagon. 

A profile of the common rafter must also be drawn 
from which a pattern can be made for laying out the 
jack rafters and also to allow developing a profile of 
tlie hip rafter, Figure 100. Draw a base line, and from 
the center point G draw a perpendicular line. On the 
base line, from the center point G, mark off the run of 


HOW TO FRAME A CURVED RAFTER ROOF 


225 


a common rafter, 8%", as at 11. The run is taken from 
the layout G-ll, Figure 99. 

Note that the jack rafters are a part of the run and 
curve of a common rafter and although no common 
rafters are used in the framing of this roof it is neces¬ 
sary to make a complete section of the outer curve of 
the roof in order to get a refined and true roof surface. 
This can only he developed on what would he the run of 
a common rafter. 

From the center point G mark off on the perpen¬ 
dicular line 15", the total height, as at T, Figure 100, 
given in the specifications. To avoid a feather edge 
on the rafters at the extreme top, the apex is cut off 
3%" helow the extreme height and a finial, worked out 
of solid stock, continues the lines of the roof to give a 
finish. Measure down on the center line from the 
extreme height T, 14 ", and produce a short level line 
intersecting the center line. With the dividers set to 
Vs" radius, place them on the intersection of these two 
lines and scribe a circle, giving the finish at the top of 
the finial. Connect point T on the center line of the 
small circle with point H on the base line by 
means of a light construction line. With G as a center 
and a radius G-H, the run of the common rafter, 8%", 
scribe a circle from point G until it arcs the diagonal 
construction line as at X. With I as a center and the 
same radius, scribe a line approximately at Y. With T 
as a center and the same radius arc the line, locating 
the exact point F. With F as a center, still using the 
same radius, complete the ^^ ogee ,, curve or outer 
profile of the common rafter. Measure down on the 


226 


COURSE IN ROOF FRAMING 


center line from the joint of the finial 1", as at J. 
Measure in on the base line from the outer edge of 
rafter, 1*4", as at /. Connect the two points J and /, 
giving the back edge of the common rafter. Note that 
these are not fixed measurements but a matter left to 
the individual judgment of the framer. Care should be 
taken not to make the rafter weak at its narrowest 
point, nor of excessive size at the widest point. 

To Develop the Profile of the Hip Rafter .—Drop a 
perpendicular line of indefinite length from point H, 
at the intersection of the base line and outer edge of the 
common rafter. From the center point G draw the 
base line or run of the hip rafter, taking the run from 
the layout, G-E, Figure 99, 10", as G-E, Figure 100. 
If this angle is laid out accurately, the distance H-E 
should be equal to one-half the run, or 5". 

Divide the base line of the common rafter into anv 

*/ 

number of parts. The closer these lines are to each 
other, especially in sharp sweeps, the nearer will be 
the points through which the curve or profile is to be 
drawn, giving a true and fairer curve than if placed 
farther apart. Figure 100 shows the base line divided 
into twelve parts numbered 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 
11 and 12. Parallel to the center line draw construction 
lines extending from the base line to the top edge 
of the common rafter and extending downward until 
they intersect the base line of the hip rafter. From 
center point G draw a center line at right angles to the 
base line of the hip and of indefinite length. Also at 
each one of the points on the base line draw construc¬ 
tion lines at right angles to the base line of the hip 


HOW TO FRAME A CURVED RAFTER ROOF 


227 


Profile of 

Common Rafter 


G-H 



Profile of flip Rafter 


Figure 100.—The Profile of a Common Rafter Developed on the Plan. 
The Hip Rafter Is Developed from the Profile of the Common Rafter 



























228 


COURSE IN ROOF FRAMING 


rafter and parallel to the center line. Number the lines 
for identification purposes to correspond to the numbers 
on similar lines on the common rafter. 

On the center line of the hip rafter, from the point G 
mark oft the distance from G to the joint of the finial 
on the common rafter, H 14 ". Likewise, on each one of 
the construction lines on the hip rafter mark off the 
corresponding distances on the common rafter, measur¬ 
ing in each case from the base line of the respective 
rafters to the top edge of the rafter. That is, 10-10, 
12-1,2,11-11, etc., on the hip rafter is the same distance 
as 12-12, 11-11, 10-10, etc., on the common rafter, Fig¬ 
ure 100. This gives a series of points on the construc¬ 
tion lines on the hip rafter into which small brads 
can be driven, a thin batten bent around them, and the 
profile of the hip rafter penned in. Measure down on 
the center line of the hip rafter from the joint of the 
finial 1", the same distance used on the common rafter. 
Project the bottom edge of the back of the common 
rafter 1 down to the base line of the hip rafter. Con¬ 
nect I and J, giving the back edge of the hip rafter 
that will line up with the back edge of the common 
rafter. 

To Transfer the Lines of the Layout to the Rafter 
Stock .—Joint the back edge of the stock straight and 
work from this edge instead of from the top edge as 
in laying out a straight roof. Place the stock on the 
layout and transfer the various distances marked 0 
Figure 101, along the back edge of the hip. 
Set a bevel square on the layout, Figure 100, to 
the bevel formed by the plumb construction lines and 




HOW TO FRAME A CURVED RAFTER ROOF 


229 

































230 


COURSE IN ROOF FRAMING 


the back edge of the stock. Place the bevel against the 
jointed edge and at each one of the distances marked 0 
produce a plumb line. Number to correspond to the 
layout for identification purposes. Measure the dis¬ 
tances on the layout from the back edge of the rafter, 
Figure 100, to the top edge or profile as 0-1, 0-2, 0-3, 
0-4, 0-5, 0-6, 0-7, 0-8, 0-9, O-10 and 0-11. Transfer 
these same measurements to the respective lines on 
the stock, measuring from the back edge and locating a 
point on each one of the plumb construction lines into 
which a small brad can be driven, a thin batten bent 
around them, and the profile of the hip rafter penned 
in. This method of picking up the lines is the same 
for both common and hip rafters. 

To Lay Out the Hip Rafter .—Transfer the lines of 
the profile of the hip rafter from the layout to the 
stock to be used for the hip, using the method previously 
described. Hip rafters A form a butt joint as at C, 
Figure 104, so that a pair of hip rafters should be cut 
the extreme length as at C, Figure 101. Hip rafters B 
must be beveled to fit against the side of hip rafters A. 
From the extreme length, as at (7, Figure 101, deduct 
the distance C-K, Figure 104, by measuring forward 
on a level line from plumb line C the distance C-K, 
and produce plumb line K, Figure 101. Square plumb 
line K across the top and locate the center point. 

To determine the bevel or top cut so that hips B 
will fit against the sides of hips A, measure forward 
on a level line, Figure 101, from plumb line K, the 
distance K-L, Figure 104, and produce plumb line L 
on the side of the rafter, Figure 101. Square plumb 




HOW TO FRAME A CURVED RAFTER ROOF 


231 


line L across the top edge of the rafter and from 
the opposite side of the rafter draw a bevel line 
through the center of plumb line K on the top edge, 
producing bevel 1. Cut on bevel 1 for the fit against 
the side of hips A After making the cut, place a try 
square against bevel 1 and square a line across the 
top edge from plumb line L, Figure 101. Cut on 
bevel 2 and on plumb line L for the joint between 
rafters B. 

To Back the Hip Bafter .—Draw a section of the plate 
and hip rafter full size as shown in Figure 102, which 
is an enlarged section of the hexagonal plate S-S, 
Figure 99. Where the outside edges of the hip rafter 
intersect the plate, square a line across at right angles 
to the center line as at K, Figure 102. Then J-K on 
the center line is the amount of backing to be removed 
at the various station lines. 

Produce a level line radiating from the top edge of 
the hip rafter at each plumb construction line, as at J , 
Figure 101. Measure in on each level line from the 
top edge of the rafter the distance J-K, Figure 102, as 
J.K, Figure 101. This gives another series of points 
into which small brads can be driven, a thin batten 
bent around them, and the backing line penned in. 
Note that the backing line is not parallel to the top 
edge of the rafter but varies according to the curve 
of the roof, being greater in some places than in others. 

Gauge a line through the center of the hip rafter on 
the top edge and remove the corner between the center 
line on the top edge and the backing line on the side 
of the rafter. It will be necessary to lay out the level 


232 


COURSE IN ROOF FRAMING 


lines on either side of the rafter and locate the back¬ 
ings on either side independently of each other, due to 
the fact that the backing line is not parallel to the top 
edge of the hip. 



Figure 102.—Enlarged Section Through S-S, Figure 99, Showing the 
Amount of Backing for the Hip Rafters 


To Lay Out the Jack Rafters .—The jack rafters are 
a part of the run of a common rafter. Although a 
common rafter is not used in this particular problem 
it is better practice to make a pattern of the entire 









HOW TO FRAME A CURVED RAFTER ROOF 


233 


rafter than to lay out only the particular portion 
needed. 

Take the run of jack rafter No. 2 from the plan, 
h igure 99, measuring from the wall line to the center 
line of the hip rafter, 6%". Also measure the run of 
jack rafter No. 1, 3 7/16", Figure 99. 

To determine the portion of the curve of the com¬ 
mon rafter to use for the jack rafters, measure in on 
the base line on the layout, Figure 100, the run of 
rafter No. 1, 3 7/16", also the run of rafter No. 2, 6%", 
and at these points produce a plumb line. The inter¬ 
section of the plumb lines on the profile or top edge of 
the rafter will give the desired length on the center 
lines for the respective jack rafters shown in the en¬ 
larged view, Figure 103. From this length deduct 
one-half the thickness of the hip rafter measured on 
the line of the jack rafter or one-half the diagonal 
thickness of the hip as shown in the enlarged section, 
Figure 104, which is a vieAv through W-W, Figure 99. 
Draw a full size section of the hip and jack rafters 
as shown and where the outside edge of the jack rafter 
intersects the outside edge of the hip rafter square a 
line across at right angles to the center line of the 
jack rafter as shown in Figure 104. To determine 
the cutting length of the jack rafters measure in on a 
level line, Figure 103, from plumb line M, the extreme 
length of the rafters, the distance M-N, Figure 104, 
and produce plumb line A 7 on the side of the stock. 
Square this line across the top edge and locate the 
center point. 

To determine the bevel or top cut so that the jack 


234 


COURSE IN ROOF FRAMING 



r-*- 



















HOW TO FRAME A CURVED RAFTER ROOF 


235 


rafter will fit against the side of the hip rafter at 
the proper angle measure in on a level line, Figure 
103, from plumb line N the distance N-O, Figure 104, 



Figure 104.—Enlarged Section Through S-S, Figure 99, Showing the 
Intersection of the Hip Rafter. Also Enlarged Section Through 
W-W, Figure 99, Showing Intersection of Hip and Jack Rafters 


and produce plumb line 0 on the side of the rafter. 
Connect plumb line 0 through the center of plumb line 
N on the top edge as shown in the top view, Figure 
















236 


COURSE IN ROOF FRAMING 


103, at 1. Cut on the curved line for the top edge of 
the jack rafters and on plumb line 0 and bevel 1 for 
the fit against the side of the hip rafters. 

To Assemble the Roof .—Assemble the rafters as 



Figure 105. Elevation of Curved Rafter Roof, Showing the Method of 

Framing 

shown in the elevation, Figure 105. Set up hip rafters 
A, then hip rafters B and lastly the jack rafters spaced 
2" on centers. The top edge of the jacks and center 
lines of the hip rafters should be in perfect alinement. 









CHAPTER X 


HOW TO FRAME A CONIC ROOF 

A conic roof is a roof having a shape like a cone, 
circular at the base and tapering to a point. It af¬ 
fords a study in laying out and fitting sweeps and in 
methods for developing the exact shape and bevels for 
the covering boards, either vertical or horizontal. 

Specifications. —Plate, %" x 1%" doubled. 

Hip rafters, %" x I 14 ". 

Circular ribs, %" x 114 ". 

Sheathing, %". 

Dimensions (see plan, Figure 106). 

Layout .—A full size working layout of the plan, 
Figure 106, should be drawn on a board or a sheet of 
detail paper. Lay out the elevation first and project 
the various points down to the plan or base of the 
roof. Produce a base line as at A and a center line B, 
Figure 106, from which to start the measurements. On 
the base line lay off 12" on either side of the center 
line B, giving the total span to the outside of the 
sheathing. On center line B lay off the total height, 
36", measuring from the base line as at C. Connect 
the point C with the points on the base line, giving 
the desired outer shape of the cone as at D. Parallel 
to these lines lay off %" thickness of sheathing and 
IVj" width of the rafter stock. Measure up on the 
center line from the base line %" twice, the thickness 

of the plate doubled, and lay in lines parallel to the 

237 



238 


COURSE IN ROOF FRAMING 



Figure 106.—Plan of Conic Roof, from Which the Working Layout Is 

Made 










































HOW TO FRAME A CONIC ROOF 


239 


base line. From the top of the plate measure up 8" 
(the distance between the plate and first rib) %" 



Figure 107.— (1) Details of Finial. (2) Enlarged Section Showing 
Method of Intersecting the Rafters. (3) Developed Upper End of 
Rafters B, Showing Method of Fitting Them Against the Sides 

of Rafter A 

thickness of rib, 10" distance between first and second 
rib and %" thickness of rib. Through these points 
draw lines parallel to the plate. 
























240 


COURSE IN ROOF FRAMING 


To avoid bringing the sheathing boards to a feather 
edge at the extreme point the rafters are cut off 4" 
from the extreme high point and a finial continues 
the lines of the outside of the sheathing, giving a 
better finish as at 1 , Figure 107. If blocking %" 
square is inserted as shown it will make a stronger 
binding in fastening the rafters together. 

The next step is to lay out the plan shown in the 
bottom view, Figure 106. Continue the center vertical 
line B down an indefinite length and at a convenient 
distance draw a horizontal center line. Project 
the various distances on the elevation down until thev 

t/ 

intersect this center line. Set the trammels at these 
points and draw the various lines showing the out¬ 
side and inside of the sheathing and the inside and 
outside lines of the various ribs. At an angle of 
forty-five degrees to the center line draw in the center 
lines of rafters 7 and on each side of the center lines of 

3 14.t one-lialf the thickness of the 

stock used for the rafters and mark in the outside edges 
of the rafters as shown in the bottom view, Figure 106. 

To Lay Out Pattern for Sweeps .—It will be neces¬ 
sary to make patterns of the horizontal ribs or sweeps 
for use in marking out the sweeps. One pattern will 
do for each sweep. Sixteen pieces are required to 
frame plate E and eight pieces each for ribs F and G. 
The length of the sweeps for the plate is from center 
to center of each rafter. The length of the sweeps 
for ribs F and G is from inside to inside of each 
rafter, making due allowance on either end for fitting 
them into place. 


HOW TO FRAME A CONIC ROOF 


241 


Lay tlie stock to be used for the patterns on the 
layout and with the trammels set to the respective 
radii used in making the layout, and the same 
center, mark out the pattern. Place the patterns on 
the stock to he used for the roof and mark out six¬ 
teen pieces for plate E and eight pieces for each of the 
sweeps F and G. Tilt the hand-saw table to the required 
pitch and saw to the lines in cutting out sweeps F and 
G y allowing at least an eighth of an inch on either end 
for fitting. In cutting out sweeps E allow about %" 
on either side of the line. Fit the sweeps for the plate 
together over the lines on the layout, doubling and break¬ 
ing the joints, fastening them well together and keeping 
the nails well back from the lines. Before taking the 
plate off the layout, again mark accurately with the 
trammels using the same center employed in making 
the layout. Take the plate off the layout, cut the out¬ 
side line to the required pitch on the band-saw and 
the inside line on the jig-saw. 

To Lay Out the Rafters .—Place the stock to be used 
for the rafters over the rafter lines on the layout. 
Mark the bottom bevel against the plate and the top 
cut against the blocking. Cut four rafters H to this 
size as shown in the plan, Figure 106. The four 
rafters 7, crossing at an angle of forty-five degrees, 
are beveled to fit against the sides of rafters 77. The 
rafters are the same length on the center lines. To 
lay out the top bevel measure back on a level line 
from the extreme length B, Figure 107, a distance 
equal to one-lialf the thickness of the stock used, %" and 
produce another plumb line as at C. Connect plumb 


242 


COURSE IN ROOF FRAMING 


line C with the center point on plumb line B as shown 
on the top view at D. 

To Assemble the Rafters —Assemble the rafters as 



I igure 108.—Elevation of Conic Roof, Showing Method of Framing 

shown in Figure 108. Set up rafters H first, with the 
blocking between, securely fastening them at the plate 
and tying them well at the top. Then set up rafters 






HOW TO FRAME A CONIC ROOF 


243 


I, fastening them well at the plate and against the sides 
of the four main rafters. Mark the stations on the 
rafters, locating the positions of the ribs as taken from 
the layout. Fit the sweeps in between the rafters, 
securely fastening them, and the roof is ready for 
sheathing. 

To Determine the Shape and Size of the Sheathing or 
Covering Boards .—To find the exact shape and bevels 
for the outside covering or sheathing hoards, divide a 
section of the plan between center lines on the outside 
line of the sheathing into a number of equal parts as 
shown on the plan, Figure 106. These distances should 
be equal to the desired width of the stock to be used 
for the sheathing. The sheathing should be as wide as 
possible, or as wide as the sweep of the plate allows. 
If the sweep is flat the sheathing can be wider than 
for a quick sweep, otherwise it may be necessary to 
hollow out the back of each board in order to have it 
ride properly on the frame work. Considerable dress¬ 
ing mav be avoided in finishing the outside surface of 
the sheathing if narrow stock is used. 

The length of the sheathing is determined by de¬ 
veloping the curve of the roof on the sheathing line. 
With C as a center and C-D as a radius draw part of 
a circle as shown on the elevation, Figure 106. On 
this curve lay off distances equal to the divisions made 
on the plan or desired width of the sheathing. Connect 
these points with the apex at 0. This gives the exact 
shape and size of the sheathing to the plate level, to 
which must be added the necessary projection. Make 
a pattern to the shape on the layout and mark out 



244 


COURSE IN ROOF FRAMING 



forty-eight pieces. The pattern can also be used in 
cutting the stock out on the circular saw by tacking 
the pattern to the stock and running the pattern 


Figure 109.—Elevation of Conic Roof, Showing Method of Sheathing 

against the fence. The table should be tilted to under¬ 
cut the edge so that the stock will hug the sweep of 
the plate properly. To determine the amount of 
undercut connect one of the divisions laid off on the 
plan with the center as shown on the bottom view, 







HOW TO FRAME A CONIC ROOF 


245 


Figure 106, also draw a straight line from one division 
to the other. Set a bevel to these two straight lines 
and apply the bevel to the top surface of the stock 
used for the sheathing and bevel to fit. 


CHAPTER XI 


HOW TO DEVELOP HOPPER BEVELS 

A hopper is a trough usually shaped like an inverted 
cone, the sides of which splay out from the bottom. 
Splayed work, as it is termed in joinery, denotes a 
surface sloping away from, or toward, other surfaces. 
Such work is often found in jambs, sills, sides of win- 



Figure 110.—Assembled Hoppers, the One on the Left Showing a Miter 
Joint; the One on the Right a Butt Joint 

dows or doors, hoods over fire-places, etc. A hip roof 
is nothing more than an inverted hopper requiring a 
knowledge of hopper bevels to properly intersect the 
roof hoards on a hip rafter and for laying out the 
side and top cuts for gutters intersecting on a hip- 
rafter roof. 


246 











HOW TO DEVELOP HOPPER BEVELS 


247 


Figure 110 shows two boxes the sides of which splay 
out from the bottom. The sides of the box on the left 
are mitered at the corners. The sides of the box on 
the right are hutted together at the corners. 



Figure 111.—Graphic and Steel Square Method for Determining a Miter 

Joint for a Hopper 

Miter Joint .—To develop the bevel for a miter joint 
on the square edge of the stock to be used for the 
hopper draw in a section of the hopper, full size, as 
shown at the left, Figure 111. D-F, 4 3/16", is the width 

























248 


COURSE IN ROOF FRAMING 


of stock required for a side. E~F is the amount of 
stock to be removed in producing a level line for the 
finished top edge. 

At a convenient distance above the side view, draw 
two lines a distance apart equal to the thickness of 
the stock to be used. Project a line up from the point 
E and also from G until it intersects the top view as 
shown on the left hand side of Figure 111. Connect 
the two points thus obtained for the intersecting miter 
cut. The miter can also be laid out with the steel square 
as shown on the right hand side. Figure 111, by using 
the rise A-B, 3 y 2 ", on the tongue and the length C-B, 
3 15/16" (bridge measure of the run and rise) on the 
blade. Mark on the tongue for the miter cut. 

To lay out the side of the hopper use the run A-C, 
1%", on the tongue and the rise A-B, 3%", on the blade. 
Mark on the tongue for the splay of the side. Measure 
on the level line E in laying oft the length of the 
sides, 8". Cut four sides exactly the same length and 
remove the corners E-E before fastening together. 

If a bevel square is set to the miter as developed 
on the top edge and used in testing the joint while 
dressing for a perfect fit it will be necessary to hold 
the stock of the bevel at all times parallel to the top 
edge of the hopper. This is rather difficult to do and 
the trouble can be overcome by developing the bevel 
shown at the bottom left hand side of Figure 111. The 
bevel square, if set to this developed bevel, can be 
applied at right angles to the side of the stock and 
tested in the same manner that a try-square is used 
in testing a square edge. Draw the horizontal line E 


HOW TO DEVELOP HOPPER BEVELS 


249 


on the development a convenient distance below the 
side elevation. Measure the distance E-D on the side 
view, make the distance E-D on the development the 
same, and draw in the base line D. Carry the point E 
on the side view down until it intersects level line E 
on the development. Carry the point D on the side 
view down until it intersects base line as at H. Con¬ 
nect E-EL, giving the splay of the hopper. Carry the 
point G on the side view down until it intersects the 
top line E on the development as at I and from this 
point produce a line parallel to E-El as 1-J. At right 
angles to these lines draw in two parallel lines a dis¬ 
tance apart equal to the thickness of stock used in 
constructing the hopper and connect the points thus 
obtained and shown in the development, bottom left 
hand side of Figure 111. Then angle L on the top view 
is the miter cut laid oft on the top square edge of 
the stock and angle K is the angle at which to set the 
bevel square for testing the joint for a perfect fit, 
holding the bevel at right angles to the edge. 

Butt Joint .—To develop the bevel for a butt joint 
on the square edge of the stock, draw in a section of 
the hopper, full size, as shown at the left, Figure 112. 
D-F, 4 3/16", is the width of stock required for a side. 
E-F is the amount of stock to be removed in producing 
a level line for the finished top edge. 

At a convenient distance above the side view draw 
two lines a distance apart equal to the thickness of 
the stock to be used. Project a line up from the 
point F and also from E until it intersects the top 
view as shown on the left hand side, Figure 112. Con- 



250 


COURSE IN ROOF FRAMING 


nect the two points thus obtained for the intersecting 
butt joint. This butt joint can also be laid out with 
the steel square as shown on the right hand side of 
Figure 112 by using one-half the run A-C, 1%", or 



Figure 112.—Graphic and Steel Square Method for Determining a Butt 

Joint for a Hopper 


%" on the tongue, and the length C-B, 3 15/16" (bridge 
measure of the run and rise) on the blade. Mark on 
the tongue for the butt joint. 

To lay out the side of the hopper use the run A-C, 
1 3 4 ", on the tongue and the rise A-B, 3%", on the 
blade. Mark on the tongue for the splay of the side. 




























HOW TO DEVELOP HOPPER BEVELS 


251 


Measure on the level line E in laying 1 off the length 
of the sides, 8'. The two ends should be cut twice the 
distance E-M shorter than the sides. Remove the 
corner E-E before fastening together. 

If the bevel square is set to the butt joint as de¬ 
veloped on the top edge and used in testing the joint 
while dressing for a perfect tit, it will be necessary to 
hold the stock of the bevel parallel to the top edge of 
the hopper at all times. This is rather difficult to do 
and the trouble can be overcome by developing the bevel 
shown at the bottom left hand side of Figure 112. 
The bevel square, if set to this developed bevel, can 
be applied at right angles to the side of the stock and 
tested in the same manner that a try-square is used in 
testing a square edge. 

Draw horizontal line E on the development a con¬ 
venient distance below the side elevation. Measure 
the distance E-T) on the side view, make the distance 
E-D on the development the same, and draw in the 
base line D. Carry the point I) on the side view down 
until it intersects the base line as at G. Carry the 
point E on the side view down until it intersects level 
line E on the development. Connect H-G, giving the 
splay of the hopper. Carry the point F on the side 
view down until it intersects the top line E on the 
development as at 7 and from this point produce a 
line parallel to G-H, as I-J. At right angles to these 
lines draw in two parallel lines a distance apart 
equal to the thickness of stock used in constructing the 
hopper and connect the points thus obtained and shown 
in the development, bottom left hand side, Figure 112. 


252 


COURSE IN ROOF FRAMING 


Then angle K on the top view is the bntt joint laid oft 
on the top square edge of the stock and angle L is the 
angle at which to set the bevel square for testing 
the joint for a perfect fit, holding the bevel at right 
angles to the edge. 


CHAPTER XII 

HOW TO MITER RAKE AND LEVEL MOULDINGS 

A raking mould is a term used for mouldings which 
are inclined; as, in a gable, a moulding following the 
pitch or slope of the roof. To make a miter between 
a rake moulding and a level moulding the profile or 
outline of one of them must he modified. The cut for 
the level moulding is an ordinary miter cut, or angle 
of forty-five degrees. The cut for the rake moulding 
is the same as a jack rafter top and side cut. These 
cuts can best he made in a miter box, using either the 
graphic method, Figure 115, or the steel square, Figure 
116, in laying out the cuts. 

To determine the profile or outline for a raking 
moulding proceed as shown in Figure 113. Draw the 
normal moulding i, extending the upper and lower 
fillets diagonally to correspond to the pitch of the roof 
on which the moulding is to be used. The profiles 
will vary as the pitch or slope of the roof changes. 
Divide the outline of moulding 1 into any number of 
parts and from these points of division erect perpen¬ 
dicular lines until thev intersect the horizontal line 

«/ 

A-B-C. From these same divisions on the outline of 
the moulding draw in lines parallel to the raking or 
diagonal pitch lines of the roof. 

To determine the profile of a moulding which may be 

applied to the rake or gable, the members of which will 

intersect and miter with moulding 1, mark off on the 

253 


254 


COURSE IN ROOF FRAMING 



Figure 113.—Method for Developing the Profile or Outline of Rake 
and Level Mouldings, so That the Various Members Will Intersect 

When Mitered 











HOW TO MITER RAKE AND LEVEL MOULDINGS 


255 


pitch line a short distance from moulding’ 1 the various 
divisions A-B-C, moulding 2, Figure 113, making ex¬ 
actly the same number and size of parts. This can be 
very easily done by marking the divisions on a strip 
of paper and transferring them. From these points 
of division on the raking line, draw lines at right angles 
to the pitch as at C-D, moulding 2. The intersection of 



Figure 114.—Making Plumb Cut on Rake Moulding in Miter Box, and 

Illustrating the Assembled Mouldings 

these lines with those drawn parallel to the rake of 
the moulding will give the points through which the 
profile of the raking mould may be drawn so that it 
will member and intersect with the level moulding. 

The return profile which occurs near the top of an 
open pediment may be determined in the same man¬ 
ner. A short distance from moulding 2 produce 




256 


COURISE IN ROOF FRAMING 


plumb line C-D, moulding 3, Figure 113. Mark off on 
a level line the various distance A-B-C, moulding 1 , 
making exactly the same number and size of parts, 
using a strip of paper as suggested for transferring 
them. From these points draw in plumb lines parallel 
to C-D. The intersection of these lines with tlios*e 
drawn parallel to the rake of the moulding will give 
the points through which the profile of the level mould- 


Mitre Cut fori Mitre Cut for' 

Level Moldinqj) Rake Mold. 

^/ y ~ *z 1 

^ a * 


-7-1 t 


Jop View| 

! ! . 


Kl\ 

k3_ _[ _ _ _ 


Side View 



End View 


Figure 115.—Miter Box, Showing Graphic Method for Laying Out Top 

Cut for Rake Moulding 


ing mav be drawn so that it will member and intersect 
with the raking moulding. 

Figure 114 illustrates the assembled moulding and 
shows the method of cutting the rake moulding in the 
miter box. Straight stock was used in the illustration 
to simplify the demonstration of the principles in¬ 
volved. 

To miter level mouldings 1 and 3 use an ordinary 
miter box, placing the moulding in the box similarly to 
any crown moulding. To miter rake moulding 2 use 





















257 


HOW TO MITER RAKE AND LEVEL MOULDINGS 

the same method for determining the cut as that used 
in laying out the cheek and top cut for jack rafters. 
Draw a plumb line on the side of the box as shown in 
Figuie 115. Pai allel to it draw another line a distance 
apart equal to the width of the miter box, making the 



distance A on the side of the box and A on the top of 
the box the same. Square these two plumb lines across 
the top of the box and connect diagonally as shown in 
Figure 115. Place the moulding in the box similarly 
to any crown moulding. 

These cuts can also be laid out with the steel square 
as shown in Figure 116, using the rise in inches per 





























258 


COURSE IN ROOF FRAMING 


foot, 10" (this problem illustrating a 5/12 pitch roof) 
on the tongue and the run, 12" (the unit for one foot 
of run) on the blade. Mark on the tongue for the cut 
on the side of the box. To determine the top cut use 
the run, 12", on the tongue and the length, 15%" 
(bridge measure of the rise 10" and the run 12") on 
the blade. Mark on the blade for the miter or top cut. 


QUESTIONS FOR REVIEW 
WITH KEY TO THE QUESTIONS 

(1) Define the term Run; Rise; Pitch. (See page 16.) 

(2) Define Projection; Wall Line; Facia Line; Span. 

(See pages 18 and 19.) 

(3) Define the term Plancher Level; Rirdsmouth. 

(See page 18.) 

(4) What determines the pancher level! The plate 

level! (See page 18.) 

(5) Define the term Ridge. What is its purpose! 

(See page 19.) 

(6) Define the terms Hip Rafter; Valley Rafter; 

Common Rafter; Jack Rafter; Cripple Rafter. 
(See page 19.) 

(7) Give a description of an adjustable fence. For 

wliat purpose is the fence used! (See pages 
23, 24 and 25.) 

(8) What lengths are obtained with the fence and 

steel square! (See page 23.) 

(9) Where should the measurements be taken on a 

rafter! Why! (See page 21.) 


QUESTIONS FOR REVIEW 


259 


Wliat is the best scale to use in laying out the 
plan of a roof? Why? (See page 28.) 

Why should the rafters he numbered on the plan 
as well as on the rafter? (See page 29.) 

What is a gable roof? (See page 31.) A hip 
roof? (A hip roof is a roof having both sloping 
sides and sloping ends.) 

What unit is used in laying out common rafters? 
(See page 25.) 

What unit is used in laying out hip and valley 
rafters for roofs of equal pitch? (See page 45.) 

How is the rise in inches per foot determined 
when the total run and rise is given? (Rise 
in inches divided bv the run in feet.) 

What deductions must be made from the extreme 
lengths of common or jack rafters intersecting 
with a ridge? (See page 23.) 

What deductions must be made from the extreme 
lengths of jack rafters intersecting with a hip 
or valley? (See page 23.) 

What deductions must be made from the extreme 
length of hip and valley rafters intersecting 
with a ridge? (See page 23.) 

What deductions must be made from the extreme 
length of hip and valley rafters intersecting 
with another hip or valley rafter? (See 
page 23.) 

How is the top cut for a jack rafter intersecting 
with a hip or valley rafter determined on a 
roof of equal pitch? (See pages 41 and 42.) 


260 


COURSE IN ROOF FRAMING 


On roofs of unequal pitch? (Oil roofs of un¬ 
equal pitch, pick up bevels from the lay out.) 

(21) What figures are used on the square for laying* 

out the top cuts for jack rafters? (See page 
42.) 

(22) What is meant by backing a hip rafter? What 

is the rule for backing? (See page 49.) 

(23) Wliat is meant by dropping a hip rafter? What 

is the rule for dropping? (See page 50.) 

(24) How is the backing determined on roofs of un¬ 

equal pitch? (See Figure 65.) 

(25) Why is the plate level higher on one side of a. 

building than on the other side with roofs of 
unequal pitch? (See Figure 56.) 

(26) What is a gambrel roof? (A gambrel roof is 

one with a gable whose slopes are broken so 
that the lower slope finishing at the eaves is 
steeper than the upper slope.) 

(27) Show by sketch the proportions for laying out 

a gambrel roof. (See Figure 87.) 

(28) Show by diagram how the length of all common, 

jack and cripple rafters for roofs of equal 
pitch may be obtained. (See Figure 96.) 

(29) Show by diagram how the length of hip and 

valley rafters may be obtained. (See Figures 
97 and 98.) 

(30) Show by sketch the method for laying out a pro¬ 

file of a common rafter for a curved rafter 
roof. (See Figure 100.) 

(31) Show by sketch the method for developing the 


QUESTIONS FOR REVIEW 


261 


profile of a hip rafter from the common rafter 
for a curved rafter roof. (See Figure 100.) 

(32) Show by sketch how the backing- is determined 

and applied for a curved rafter roof. (See 
Figures 101 and 102.) 

(33) Show by sketch the method for determining the 

length and shape of sheathing or covering for 
a conic roof. (See Figure 106.) 

(34) Show by sketch how the butt joint for a hopper 

is determined. (See Figure 112.) 

(35) Show by sketch how the miter joint for a hopper 

is determined. (See Figure 111.) 

(36) Show by sketch how moulding profiles are devel¬ 

oped for intersecting rake and level mouldings. 
(See Figure 113.) 

(37) Show by sketch how the intersecting miter is 

determined for rake and level mouldings. (See 
Figures 115 and 116.) 




INDEX 


Adjustable fence, 23 

Bevels, hopper, how to develop, 
246 

Birdsmouth, 18 
Butt joint, 249 

Common rafter, 19 
Common rafter, to lay out, 33 
Conic roof, how to frame, 237 
Cripple rafter, 19 
Curved rafter roof, how to frame, 
222 

Curved rafter roof, elevation of, 
236 

Dormers, 164 

Facia line, 19 
Fence, adjustable, 23 
Fence, application of, 25 

Gable roof, 31. 

Gambrel roof, how to frame, 191 

Header, to determine the side and 
top cut of, 185 
Hip rafter, 19 

Hip rafter, to back, 49 

Hip rafter, to lay out, 45 

Hip rafter, to drop, 50 

Hopper bevels, how to develop, 
246 

Jack rafter, 19 
Jack rafters, to lay out, 41 
Jack rafters, developed length of, 
234 


Lengths of common, jack and 
cripple rafters, diagram for ob¬ 
taining, 216 

Lengths of roof rafters, how to 
determine, 215 
Lines, 15 

Measurements, 20 
Miter joint for a hopper, 247 
Mouldings, rake and level, how 
to miter 253 

Pitch 16 
Plancher, 18 
Plancher level, 18 
Plate level, 18 
Problems for practice, 59 
Projection, 19 

Rafters, development of on plan, 
55 

Rafters, run and length of, 36, 57 
Rake, 18 

Rake and level mouldings, how 
to miter, 253 
Ridge, 19 

Ridges, to lay out, 52 

Rise, 16 

Roof, gable, 31 

Roof framing, principles of. 15 
Roof framing terms, 15 
Roof, to assemble, 5 
Roof of equal pitch, how to frame, 
37 

Roof of unequal pitch, how to 
frame, 127 
Run, 16 


Laying out, 27 Sheathing, to determine shape 

Lengths of hip and valley rafters, and size of, 243 
diagrams for obtaining, 218, 220 Span, 18 

263 


264 


INDEX 


Sweeps, to lay out pattern for, Valley rafter, 19 

240 Valley rafter, to lay out, 50 

Unequal pitch roof, how to frame, 

127 Wall line, 19 

Unequal pitch roof with dormers, 

164 








4 








